Evidence internal to the texts, for the most part. Most of it is historical narrative in one form or another, but any time historical narrative is attempted (even now) there is tension between the "facts" and the narrative structure. Basically, the degree to which facts are allowed to stand in the way of a good story has varied considerably over time and place and the literary agenda of the author. Of course, you will say that God could not have inspired such a narrative, it must be 100% accurate literal history for you to allow it divine inspiration. But nobody wrote history like that then and nobody expected it and they thought it was "true" anyway.
Most of the discussions we get into about Genesis are really just about the Garden story, which is clearly a form of historical narrative known as an etiology. All cultures produce them, because all peoples desire to know the answers to the same basic questions: Where did we come from? Why are we here? Why are things always so screwed up when we know they could be better?
You can believe if you like that of all the hundreds of such stories the Garden story is the one and only which is also "100% accurate factual history," but it doesn't matter, really. For centuries people believed that the story was more or less true in the absence of information to the contrary, but that's not why the story was important to them, that's not why God told us the story to begin with.
Evidently versions of it survived as oral tradition before it was finally written down. The elements desired by a professional story teller are all there; puns and other wordplay, the anthropomorphization of non-human characters, etc. It would make a good panto. You would need a story-teller, some musicians, and three or four actors with masks and simple props all on a square of carpet rolled out in the souk. Add some topical references, bawdy asides and other horseplay and at the end the angel chases Adam and Eve into the crowd with a sword, Ta Daa. I would sure throw down a coin to see it.