Is there any historical or archaeological evidence for the Tower of Babel story or is it all pure myth?
The storytellers of some of the fables in the Bible got their origins or ideas from things that were happening around them. There is archaeological evidence of a tall building in ruins in Babylon. But this Fable was heavily embellished and It obviously could not possibly be true much like the Fable the great flood or The Exodus.
There is of course one very easy simple explanation for the myth. Which is very general and does not require you to take any part of the Bible literally. And that is simply that the whole story, is just a written down memory, of some technically primitive, rural, perhaps nomadic, people's reactions, to their first encounter with a big city. Where there are, to them, unbelievable tall buildings and an impossible to understand cosmopolitan, multicultural, multilingual population. Could be any big city anywhere, in any age.