So my response doesn’t go into your examples of Greeks or Egyptians, but I will answer in the ways and areas of historical study that I am more familiar with.

So. The idea of what constitutes a “nation” can be a somewhat difficult question to answer. I am a personal fan of Benedict Anderson’s theory of an Imagined Community (from his book Imagined Communities). To do a terrible disservice to Anderson and a wonderful book: he posits that the modern Nation as we envision it is largely a result of print capitalism, mass vernacular literacy and democracy. He essentially argues a nation is essentially a social construct formed by shared experience and language across geographical areas. Using language and cultural heritage as a counter point against ones neighbors, members of such communities are able to fabricate communal ties and an occasionally heavily edited or entirely fabricated communal history that forms something that encompasses large groups of people. Anderson has lots of interesting, thought provoking examples, but I thought some of his writings on the American founding fathers and other colonial frontrunners from around the world was really interesting. The idea being that through the shared experience of going to the colonizing country for education, the upper class and highly educated members of colonies formed stronger national identities of their own due to their experience as outsiders in the lands of their host colonies.

There is another school of thought, the primordialists I think they are called, that basically argues the opposite and hold that ideas of nationality in some form or another are the essentially basis of all human society or something. I won’t belabor the point with a long straw man argument as I’m not well read on their literature, but I think what’s important about Anderson’s theory is that it makes clear that an imagined community is much larger than say tribalism. This is because it requires the formation of an imagined community so large that there would be little to no way to feasibly meet or know all members.

With regards to my area of expertise, Japanese early modern history can be very broadly described as an attempt recreate Japan as a modern nation state. There was a huge amount of time and academic energy devoted to the formation of the Japanese national essence. There was a very influential and historically significant booklet called Kokutai no Hongi (Foundations of our National essence) distributed in Japan in the 1930s and 40s which does a lot of the things Anderson describes. I won’t quote too much, as translated Japanese tends to drag on for a million years and can get mired in never ending tiers of honorifics and circular speech that are translated too literally for my taste, but there is one selection from “On Loyalty and Patriotism” that bears posting here. (Also just to make it clear I am quoting from a Columbia online article about Kokutai no Hongi as I left my paper copies of these sources at my home in the states)

“Our country is established with the emperor, who is the descendant of Amaterasu Ōmikami, as it’s center, as our ancestors as well as we ourselves constantly have beheld in the emperor the fountainhead of her life and activities. For this reason, to serve the emperor and to receive the emperor’s great August will as our own is the rationale of making our historical “life” live in the present; and on this is based the morality of our people.”

This is a very small slice from a very long booklet (iirc it is nearly 150 pages or so) but you can see the implications when using Anderson’s theory as a lens. The document itself is creating an imagined link here in the emperor and an unverifiable link to a historic past with the emperor as its nexus. This connection is used as the basis for describing and defining what it means to be Japanese and create an in group and an out group with easily defined borders. Japanese people are all connected because of their shared connection with the emperor and the emperor and what the emperor stands for is the guiding spirit of what it means to be Japanese.

Sources include Anderson’s Imagined Communities Kokutai no Hongi 国体の本義

Note: not capitalizing the word emperor is a stylistic choice made by me even in the translated original. Although Japanese allows for no such thing as capitalization the word itself should for all intents and purposes likely be translated to reflect the veneration for the emperor in the original. I personally do not agree with the undue deification of the emperor’s position although have great personal respect for some emperors throughout history do not, as a rule, capitalize the title in unbridled reverence for the position.

It's certainly somewhere in between. The concept of nationality has existed since ancient times, but it's important to note that the ancient concepts of nationality were not the same as the concepts of 18th-19th century romantic nationalism and 19th-20th century scientific racism. It would have been extremely uncommon for anyone in the ancient world to believe that nationality and ethnicity were or should be the main organizing principles of society, or that it is somehow proven that their particular nationality is the best in the world of something like that.

I can think of several pre-modern examples where nationality (as distinct from political citizenship) is a factor or invoked as a factor.

1. Herodotus recounted the appeal of the Athenians to the Spartans for assistance against the Persians, and one of several principles the Athenians appealed to was Greek nationality.

2. The reaction of the Tang Dynasty to the An Lushan rebellion ended up degenerating into ethnic cleansing, with reprisals against non-Han people, even if they were culturally Chinese for generations and had nothing to do with the rebellion.

3. The interactions between the Ptolemaic Greek elite and the local Egyptian population, and the subsequent discord between the Melkite and Coptic churches under Roman and Muslim rule pretty clearly had an ethnic/national component.

4. During the Crusades the German crusaders felt poorly served by the institutions built by and for the Anglo-French leadership, and created the Teutonic (German) Order first to serve their medical needs, then so they could have their own military order.

This doesn't mean "nations are the oldest way people have identified themselves", which is unknowable but almost certainly not true. It also doesn't mean that people believed every nationality should have a geographical state, or anything like that, but I think it does mean that in settled societies for at least the past few thousand years, people would have been aware of the idea that one might have a nationality/ethnicity which is not solely a function of their language/religion/citizenship/place of residence, and probably has something to do with who their ancestors were. That doesn't mean nationality is immutable either. We see examples in history of ethnicities (I'm thinking of Isaurians for example) who were clearly considered distinct from the Romans in the 5th century, but at some point assimilated to the point where that ethnicity ceases to exist and they're just Romans.