You're using the phrase "ethnography" in your title but based on your description, it sounds like you mean to say "archaeology." Ethnography is a kind of research employed by anthropologists to study present-day cultures through a combination of interviews, surveys, and "participant observation" (living and participating in people's cultural activities). Archaeology is the study of the human past through scientific analysis of the material remains of past cultures. In the United States and other Western Hemisphere countries, these are both typically studied through the department of Anthropology, so it's easy to confuse the two.

A Brief History of Archaeology

Terminology out of the way, to answer this question we're going to first need to walk through a brief history of archaeology. Archaeology is a very recent scientific discipline; it has its origins around the turn of the 20th century. Like a lot of scientific disciplines, it emerged out of a pre-scientific discipline called "antiquarianism." When you're talking about 19th century Egyptologists, these would be antiquarians. The transition to scientific archaeology happened with the later introduction of methods from fields like geology and paleontology.

Antiquarianism can basically be summarized as "rich white dudes collecting weird stuff and putting it in a room to show off to their other rich white friends." This tradition started in the 16th century but reached the height of it's popularity in the 19th century with the rise of "Cabinets of Curiosities" or simply "Curios." Basically, if you were rich enough you would build a room in your house that basically works like a private museum. These curios weren't just stocked with artifacts, they also included fossils, taxidermy animals, and all sorts of other nick-knacks. The main point of a Curio was to show off to your guests, and this meant it helped if you could have stories to tell your guests about what these artifacts were and the people who made them. Of course, most often the stories that hosts would tell would be more fiction than reality. You find some gold diadem from East Africa and label it "the Crown of the Queen of Sheba" or something, because the goal was to entertain guests, not be scientifically or historically accurate.

Generally speaking, antiquarians did not employ any kind of rigorous methods to study these artifacts or the places where they were found. There were exceptions, though, which become more common over the course of the 19th century. Famously the antiquarian Thomas Jefferson (yes, that Thomas Jefferson) conducted a controlled excavation of an American Indian burial mound on his property using principles from scientific geology and arrived at the correct conclusion that it was artificially constructed by American Indians. But these experiments with scientific methods were not employed in a standardized way until the very end of the 19th century. By that point, C. J. Thomsen's the Three Age System (Stone Age, Bronze Age, Iron Age) was widely adopted and researchers started employing principles of stratigraphy, serriation, and so forth in a more systematic way. This marks the first actual scientific archaeology trend with the so-called "culture history school." This first school of thought would dominate archaeology through the Indiana Jones era of the early 20th century.

Why Europeans? Part 1: Antiquarianism

We can ultimately elaborate your question by dividing it into two parts, one relating to antiquarianism and one to archaeology. The first is the question of why Europeans seemed to develop antiquarianism. Europeans of the Early Modern Period obviously were not the first people to collect relics from past cultures. The Romans famously collected artifacts from Egypt. The Aztecs excavated into the ancient city of Teotihuacan to collect artifacts, and there's examples of this kind of thing from Mesopotamia to China as well. Nevertheless, a particular tradition of building and maintaining "cabinets of curiosities," and a drive to collect artifacts to fill them, seems to have developed in European culture at this time.

A historian on the Early Modern period could likely elaborate more, but I would point to two main factors here. The first is a shift in the renaissance towards an interest in Classical era texts and knowledge. There was a perception that knowledge from Greece, Rome, etc. had been "lost" and needed to be "recovered." Mostly, this renewed interest in Classics was focused on ancient texts, but this quickly translated to recovering material remains of these past cultures as well. Having knowledge of the Classical world became a mark of sophistication, as did owning a piece of it.

The second and arguably more important factor was colonialism. European nations of this era were forming massive colonial empires that came to encompass almost the entire world. These empires by their design pulled resources and wealth (including natural and cultural treasures) from conquered regions to the imperial core. For a growing elite profiting from these colonial empires, collecting a bunch of these in a cabinet of curiosities seemed to be an effective way to display both your prosperity and sophistication.

At the same time, colonialism also forced Europeans to confront a whole bunch of different cultures who lived in very different societies to Europeans. Some of these cultures appeared, to European eyes, to be "simple" or "primitive." Over the course of the 1800s, as Colonial empires reached their height and antiquarianism continued to stumble towards archaeology, a particular view emerged. It seemed that there were people in Europe's ancient past who seemed superficially similar (in terms of the tools they used, the architecture they built, etc.) to cultures that Europeans were encountering and conquering through colonialism. This gets into a much larger discussion of historiography that I don't want to have, but the punchline is that Europeans came to see these other people as "living fossils." This eventually metastasized into the theory of Unilineal Evolution: that all cultures evolve in a straight line through predictable stages in linear progression. Ergo, the thought was that understanding these other cultures and their history would provide a window onto the European past.

I think that your first question is getting at something puzzling (why did modern Europeans create museums and anthropology to relate to the ancient past/non-European cultures) but I think it is mistaken to claim that non-European societies lacked meaningful relationships to the ancient past or its material legacies in the present. I think virtually all human societies possess such relationships, although they take different forms and assume different degrees of cultural significance.

One clear example from my own area of expertise is the fad for kaozheng (evidentiary) scholarship in Qing China. China has always had a strong classicizing strand in its intellectual culture. Much like humanistic scholarship in Europe or any of the many religious traditions oriented towards sacred texts, this classicizing scholarship sought moral and philosophical truth by trying to recover the real meanings of ancient texts. By Qing times, many of these texts (Confucian/historical/etc) were more than two thousand years old, written in language that was about as intellible to the untrained as Latin would be to modern Italians, and had spawned many different competing schools of interpretation.

Qing scholars from the 17th century on developed innovative "evidentiary" techniques to attempt to resolve some of these contradictions. Some of these methods were philological and linguistic, but others were much more hands-on. Scholars would go out to find historical sites, make rubbings of ancient stelae and inscriptions, and talk with locals to record their own traditions of knowledge. This kind of scholarship (although moreso in its philological form) was enormously influential, leading to the conclusion that several key works of the Confucian canon could only have been written hundreds of years after Confucius's death. It also helped build interest in historical sites as destinations for literati excursions and as topics in gazeteers, literature, and poetry.

I bring this up to point out the clear parallels with 19th century European archeological work in the Near East, which was very much driven by a desire to shed new light on European classical and religious traditions: trying to find Homer's Troy, or provide material evidence of Old Testament stories. Perhaps a key difference is that northwestern Europeans inherited and elaborated intellectual traditions whose textual sources were from the classical Mediterranean and not their own backyard. Thus much of the museum building and ethnography you point to were conducted under the material conditions of empire and were fundamentally extractive.

In fact, the stereotyped notion that non-Europeans were oblivious or worse, destructive, of their own past helped legitimize European expeditions that essentially looted foreign or colonial sites/artifacts in the name of "preservation" or "scholarship." For example, James Hevia points out that many of the Chinese objects on display at the British Museum and Victoria and Albert Musem were literal war booty looted by the British troops who burnt the Old Summer Palace in Beijing during the Second Opium War. Similar dynamics apply to significant portions of non-European objects held in Western museums.

So This is a really interesting question, almost more of a historiographical question than a history question per se.

If history is the study of past facts, Historiography is the study of how and why we study history.

There are many reasons why we study history, perhaps as many as there are historians, and many different approaches to studying history.

In the 19th and early 20th centuries, many historians focused heavily on politics, diplomacy and war. This is sort of the "traditional" view of history. Talking about what president or great leader did what and who invaded whom.

But over time, many different schools of thought have arisen on other ways to interpret history. The french school focused on sociology and on looking at history through the lens of long term social developments and economic developments. Marxists view history through the lens of economic conflict between working and ruling classes. new social history emphasizes history on the experiences of ordinary people in the past. There are many other approaches unique to many other cultures.

Also in historiography, we have the ideas of studying "why" history is studied. What conclusions does a historian want to reach, what is their goal for conducting research, assembling information. So, we have the "how" we look at history, and along this same vein we have the question of "why" we study history, because historians often have unique and individual goals and motivations.

I think the answer to your question lies in looking at the "whys" of historical study. Why did Europeans prize ancient objects when others simply accepted them as stuff that was left around that was really old.

You are asking to some degree about the concept of "antiquities," and or "classicism." That idea arose primarily in the renissance era. In The Prince Machiavelli wrote of his interest in the classical period.

At the door I take off my muddy everyday clothes. I dress myself as though I were about to appear before a royal court as a Florentine envoy. Then decently attired I enter the antique courts of the great men of antiquity. They receive me with friendship; from them I derive the nourishment which alone is mine and for which I was born. Without false shame I talk with them and ask them the causes of the actions; and their humanity is so great they answer me. For four long and happy hours I lose myself in them. I forget all my troubles; I am not afraid of poverty or death. I transform myself entirely in their likeness.”

Renissance figures often looked to ancient Greek and Roman figures for inspiration as to their own societies. They borrowed from classical art and classical sculpture and classical ideas. They did this in part to differentiate themselves from the generations that came before them whom they viewed as somewhat backward. (although the source article I linked disputes this idea somewhat). They saw these ancient "classical" societies as better in some regards and aspired to some of the ideals set forth by these thinkers.

Elites in those time periods would often sponsor artists and other individuals to show their own wealth and political influence. (and certainly for altruistic means as well, but "because they liked it" is not usually a satisfying answer for why someone did something).

This interest in the classical period carried over into a strong societal interest in antiquities. Artifacts of ancient societies became prized possessions for the wealthy and well connected with the interest in obtaining them. The well educated had spent many of their school years reading of the societies of ancient Greece and Rome, they then often placed a high value in artifacts from ancient Greece, Rome and other places.

Sir Hans Sloane was an Anglo-Irish noble and physician who traveled in the carribean and died in 1753. He was a member of the royal society Like a number of elites in his era, he possessed an interest in natural history and the classics.

DUring his lifetime, he accumulated a collection of over 70,000 objects. 40,000 printed Books, 7000 manuscripts, drawings, coins, and various ancient artifacts from Sudan, Egypt Greece, Rome, the Middle East and the Americas. in 1748 he was visited by the Prince and Princess of Wales, who wrote of his collection:

[There were] several rooms filled with books; among them many hundred volumes of dried Plants; a room full of choice and valuable manuscripts...Below stairs, some rooms are fitted with the curious and venerable Antiquities of Egypt, Greece, Hetruria, Rome, Britain, and even America; others with large animals preserved in the skin; the great saloon lined on every side with bottles filled with spirits containing various animals. The halls are adorned with the horns of divers creatures...and with weapons of different countries...fifty volumes in folio would scarce suffice to contain a detail of this immense Museum...

Sloane was concerned that his daughters would sell off his collection piecemeal for money. So, in his will, he wrote that he would bequeath the entirety of his collection to the British Crown for a sum of 20,000 pounds (roughly 6-7 million in 2022 dollars), and if the crown refused, he would donate his collection to European continental collectors.

The Crown accepted the offer, and his 70,000 item personal collection formed the basis of what would become the world-famous British Museum in London. (alluded to both in the Brendan Frasier "mummy" movies, and in "Black Panther" for their collections of valuable ancient objects).

This answer meandered a bit, but to loop back around and summarize. During the renaissance, leading thinkers, authors and artists started drawing heavily on "ancient" ideas as ideals for society. This led to a more generalized interest in "antiquities," and particularly for elites, collecting those antiquities as a means of showing sophistication, wealth and influence. Some of these significant private collections ended up in the hands of museums.

This is actually an extremely complicated question. An ELI5 style answer would probably say: "The premise of your question is wrong. Western culture didn't come up with museums or ethnography and no culture has simply lived alongside the past." But that doesn't really explain anything at all. So lets start with a slightly different question: "How did people interact with their histories in the past?"

For a majority of history, the past could be explained through myths and legends about the creation of the world and the origins and adventures of specific ethnic groups or cultural heroes. These myths and legends would be used to legitimize the existence of given political, ethnic, or cultural ideologies. This has never stopped and still continues in every part of the world today.

There is overwhelming evidence from all over the world that indicates that people have always been interested in their pasts. In medieval Europe, stone celts and projectile points were collected by peasants during their agricultural work. The creation of these tools was attributed to everything from lightning strikes to elves and fairies. The Japanese believed that stone arrowheads were the weapons of supernatural armies that had fallen to earth and their discovery would require the ritual cleansing of the land. The Aztecs would regularly perform rituals in the abandoned city of Teotihuacan because that was where the gods had reestablished cosmic order at the beginning of their most recent time cycle. The Haudenosaunee, commonly known as the Iroquois, would collect and reuse copper tools, stone pipes, and stone projectile points collected from earlier Woodland and Archaic period archaeological sites. We recently discovered evidence that Late Paleoindian groups in the Oklahoma Panhandle would collect stone debris from earlier Clovis or Folsom culture archaeological sites (Bement et al. 2020).

In ancient Egypt and Mesopotamia, ancient buildings and artifacts were not only valued as relics relating to former periods of political power, but as a source of information about the past itself. During the Twelfth Dynasty of Egypt, royal craftsmen would copy art and architecture styles from the late Old Kingdom and would occasionally incorporate them into royal tombs. One of the sons of Ramesses II, Khaemwese, is known to have studied texts associated with abandoned religious buildings near Memphis in order to repair the buildings and revive their associated religious cults. Late Babylonian rulers like King Nabonidus would excavate and study the ruins of ancient mudbrick temples so that they could be rebuilt on their original foundations and restore their religious cults. Bel-Shalti-Nannar, one of Nabonidus' daughters, amassed a huge collection of statues and ancient texts in what Woolley describes as the oldest known museum of antiquities.

The Greeks appear to be the first to differentiate between historia, the study of the recent past by chronicling the memories of people who lived through historical events, and archaiologia, the study of the ancient past using myths, legends, oral traditions, and material remains. Archaiologia had a strong emphasis on geneology, the founding of cities, and the origins of peoples, institutions, and customs. Thucydides mentions that many of the graves that were dug up on the island of Delos during a religious purification in the fifth century BCE contained weapons and burial practices that resembled those used by the Carian people of southwest Anatolia. He surmised that the Carians inhabited the island of Delos at some point in the past. The Roman physician Pausanias wrote a "guide book" to public buildings, art, rituals, and customs of southern Greece during the second century CE.

In China, a philosopher during the Eastern Zhou Dynasty named Han Feizu ascribed what we would call Neolithic painted and incised ceramics to an earlier period in the development of Chinese civilization. Sima Qian, the great Chinese historian, spent time visiting ancient ruins and studying ancient relics while writing the Shi Ji. Confucian scholars of that time valued the systematic study of the past as a guide to moral behavior and used a perceived common heritage extending back to the Xia Dynasty (2205-1766 BCE) as a way to unify Chinese cultural and political life. Ancient relics were also collected and kept as prestige objects similar to statues and ornate vases in Mediterranean cultures.

Medieval Europe saw widespread destruction of the remains of the Roman Empire. Roman cemeteries and buildings were plundered for building materials, especially marble, to a point where marble ceased to be quarried. Cemeteries would also be plundered for gems, coins, and ivory which would be recycled into new works of art. The reuse of Roman sarcophagi for burials continued into the sixteenth century CE. However, not all the rulers of Medieval Europe were so interested in the destruction of the past. The Lombard kings of Northern Italy copied Roman epigraphy and coinage. Charlemagne revived many aspects of Roman art as a way to solidify his claim as a successor to the Roman emperors.

As you can see, history and connections to the past are often used as a way to legitimize or delegitimize aspects of the present, whenever the present might be. Medieval Europe is no exception to this. The Roman Catholic Church monopolized and regulated learning and believed that the Bible provided a complete and accurate history of humanity and the cosmos. Part of this regulated learning was a informal set of six relatively broad ideas that are still around today: Earth is of recent and supernatural origin, the physical world is an advanced state of degeneration as a result of sin, humanity/civilization originated in Mesopotamia, human standards of conduct also degenerated over time as a result of sin, the history of the world is a series of unconnected and unique events, and as a result of the previous ideas, it was not widely understood that people in the biblical times would have lived lives that were significantly different than those of Medieval Europeans.

During the Renaissance, attempts to use historical precedents to justify innovations in secular matters lead to the realization that the peoples of the past did not significantly resemble the peoples of the present. The Italian poet Petrarch realized that the cultural strength of ancient Rome was long gone and had been succeeded by an era of cultural deprivation. According to Petrarch, only the history of ancient Rome was worth studying. Emulation of the glorious achievements of ancient Rome was the best that Europe could do. (As a side note, this type of thinking is where we start to see the use of history and archaeology to create the perceived common heritage of "Western Culture") In the fifteenth century, ancient Greek texts brought into Italy from the Islamic world began to bring in "lost" information about European history. This lead to a revival in the study of ancient art and architecture and the resulting emulation thereof. Interest in this was also being pushed by the continued destruction of ancient buildings for the building materials needed for the construction of new cathedrals and noble mansions. In time, these pushes lead the nobility and clergy to begin collecting and displaying ancient works of art. They also began to fund individuals who would dig in locations that were suspected to have artifacts with historical, aesthetic, or commercial value. The sculptures uncovered by these diggings would inspire people like Michelangelo and Bandinelli to improve upon the sculpting skills of the ancient Romans. This is the birth of what we call today "Classics" or "Classical Studies". This is also when we begin seeing the use of the term "antiquarian" referring to a person who collects and studies ancient artifacts. Thus began the age of Antiquarianism or Classical Archaeology, a cousin (for lack of a better term) of modern archaeology.

Other commenters have given much better answers about how modern archaeology, anthropology, and museum studies evolved from here.

Sources:

• Bement, Leland C., Dakota Larrick, Richard E. Hughes, and Kristen Carlson (2020) Evidence for Late Paleoindian Scavenging of Early Paleoindian Obsidian, Oklahoma Panhandle. PaleoAmerica 6(2):194-198.

• Trigger, Bruce (2006). A History of Archaeological Thought. 2nd edition. Cambridge University Press.

A lot has already been written here, but you might be interested in this answer of mine on the origin of "history museums." To summarize, the first museums were rarely concerned with the sort of historical preservation that you are asking about. For them, indigenous artifacts were more a part of nature than of history, and the historical objects that were displayed were eccentric curios of dubious authenticity. Interest in historical preservation as we know it today can be traced to those two driving forces of the 19th-century: industrialization and nationalism. In both Europe and North America, industrialization, and the ensuing urbanization, threatened to erase traditional practices, pushing folklorists and ethnographers to document and preserve the vanishing cultures of rural peasants or indigenous Americans (but, of course, never questioning the political and economic choices that threatened them...). Wealthy financers similarly tried to protect remnants of the past that gave them (and therefore justified) their contemporary status. Nationalism permeated these elements and created a need to define and preserve certain things as national heritage. Henry Ford, for instance, founder of the largest historic preservation effort in the US, wasn't just interested in his personal history in small town America, but in projecting that experience as the America. And so, this concern for preservation is actually quite recent is usually saturated with political ends.