Many, many people have speculated that human-like figures in ancient mythology are actually memories of extinct hominins. Some examples that spring to mind are trolls/giants in Norse mythology (perennially suggested to be Neanderthals) or Enkidu from the Epic of Gilgamesh (again maybe a Neanderthal because, you know, he's hairy or something). However since the last of our cousin species had died out by 50,000 years ago, and the earliest surviving oral or written traditions we have only date to around 5,000 years ago, these theories aren't given much credence. It would take a lot to make a convincing case that a cultural memory had been retained for that long, and the people who throw these suggestions out there typically have nothing to offer beyond the fact that there's a passing resemblance.

There wouldn't really be anything in the historical record to that end, since the overlap predated the development of writing by thousands of years. It would be hard to tell if an ancient story about other peoples was actually inspired by such interactions, or is about something else and can just be intrepreted that way through a contemporary lens.

That said, I'd suggest bouncing this one off r/askanthropology! It's more in their wheelhouse and they might have something for you in terms of those possible myths.