All peoples "know their history," in a sense — it is an apparent human universal (or near-universal) that people structure their self-conceptions on both an individual and social level on some sense of a temporal narrative. This is why history is such a powerful and frequently controversial subject: if I tell you that your sense of history is wrong in some way that fundamentally challenges the way that history helps construct your sense of individual or cultural or political identity, that is going to disturb you!

As a slew of examples: Many Americans construct their shared national history as being about their having created a unique and exceptional state of "freedom," and are consequently unsettled by the reminders that for a large section of its history it was literally a slave state, and that even after slavery ended there were intentional barriers to freedom put in place for a majority of people living in the country. (All nations have "narratives" of this sort which are rooted in some sense of history, all of which are subject to being historical challenged or reinterpreted.) People who ascribe to religions that are based on some sense of historical events or figures — like the Abrahamic ones — are deeply committed to some understanding of how literally true those historical events or figures were (so "Jesus did not exist" is an inherently controversial historical claim). On an individual level, ask an American about themselves and you'll probably get a story that is rooted in some sense of a shared ethnic/immigrant identity ("I had an ancestor who was on the Mayflower," "my great-grandfather emigrated here during World War I," etc.) that is itself rooted in some sense of an individual past that is anchored to bigger historical events (the Mayflower, World War I, etc.).

Now, "ancient peoples" is a broad category and I don't know who exactly you have in mind. The Greeks actually wrote about "history" (e.g., Herodotus), so we know for sure it animated some of their thoughts, though what is interesting there is that we tend to distinguish the work of a "historian" (like Herodotus) from the "myths" (which are themselves historical statements of a sort) or "religious" historical narratives. Someone like Herodotus is credited with trying to interrogate these shared senses of the past and find out the "true" answer and to ask about things that people might not individually know about (e.g., the specifics of some general's thoughts and actions in a specific battle). So that is a somewhat more "academic" sense of the term "history" than what I was using before, though as I think is clear I don't actually, personally think the distinction is as important to how people integrate "history" into their mindsets (I do think it is important from a methodological perspective; what makes Herodotus a historian is not that he thinks historically — all people do — it's that he tries to generate new historical narratives based on some kind of empirical research, however inadequate his methods are by modern standards).

It is worth noting that we distinguish between the "prehistoric" and "historic" periods on the basis of a specific technology: writing. This is more about how we can interrogate these pasts, but it does indicate, I think, that once you have writing, we tend to find a lot of written "history," even if it is not what we might recognize as academic history. So we have accounts like this from ancient Mesopotamia:

“[Sargon] had neither rival nor equal. His splendor, over the lands it diffused. He crossed the sea in the east. In the eleventh year he conquered the western land to its farthest point. He brought it under one authority. He set up his statues there and ferried the west's body across on barges. He stationed his court officials at intervals of five double hours and ruled in unity the tribes of the lands. He marched to Kazallu and turned Kazallu into a ruin heap, so that there was not even a perch for a bird left.”

This particular text was from a much later generation, writing about something that happened in the past — or something they believed, or wanted to say, happened in the past. Whether it is true or not is a different question; the more interesting one is why write this down in the first place? I don't know the answer in this specific case, but generally it's because these stories serve a purpose like the one I mentioned before, whether it is emphasizing the evil of some past leader or their glory or what have you. You also have to ask who wrote it down — because no history writes itself! And that gets you into questions of who writes and why do they write and where do they write, and for many ancient literate societies the answers are "a professional scribe class writing things that justify and edify the class of people currently ruling their society."

What about preliterate societies? They clearly also had a sense of history — a lot of our earliest "literate" histories of sorts were originally part of an oral tradition of folklore and storytelling. So the Homeric epics and the Epic of Gligamesh were both composed pre-historically and passed on orally long before they were written down. We can infer from the few examples we have of such things that there were probably far, far more that got lost to time — once people stop telling a story, it dies. The thing that makes these surviving stories special is that people told them long enough and repeatedly enough that at some point they got written down, and that helps preserve them quite a bit. But of course even written information gets destroyed with time as well.

Even if you write it on a rock (which is where we get some of these "histories about how great this king/pharoah/warlord" was from ancient times), rock wears down, can be destroyed (including on purpose; [the damage to this mask](https://en.wikipedia.org/wiki/Sargon_of_Akkad#/media/File:Sargon_of_Akkad_(1936).jpg) that may have been of the aforementioned Sargon of Akkad was apparently done in ancient times by someone who did not like whatever that history stood for), can end up at the bottom of the sea, etc. And of course water destroys everything over time, paper is especially fragile, fire is especially damaging. (Though ironically, a lot of the clay tablets we have from ancient Mesopotamia exist because the buildings holding them were destroy by fire, which hardened and preserved the tablets.) And in general, the things that get preserved over long time periods don't get written down once, but again and again and again, being transferred from dying media to new media in a long chain of "people caring about it," which they don't always do. (Note that this problem does not go away with modern forms of media, and if anything, it is increased by it! Computer hard drives are far less reliable than well-stored paper or papyrus in a desert, in terms of survival of information over the long term. To keep modern "data" alive you have to continually — in a historical sense — transfer it to new media, new computers, etc. Woe to the person trying to access some document that they last saved on a disk or even CD-ROM a mere 20 years ago, a blink in history's eye!)

And all of this requires it getting written down in the first place, and we can infer that if people were telling "historical stories" for hundreds of thousands of years before writing technology existed, then most historical stories are probably lost to us.

All of which is to say that there is every reason to think that all ancient peoples probably had some sense that the "knew their history" (which we might, today, dismiss as obviously mythical, but would have been "history" to them, and a lot of what modern people today believe about their history is also mythical, though perhaps less-obviously in many cases, but not all), and they certainly must have know things that we no longer know (what we know about the ancient peoples is far less than what we don't know), and inasmuch as any communication contains "information," most of it must decidedly be lost, and in the case of written information, even the majority of that is certainly lost.