I think the evidence is pretty clear the creation and flood stories were borrowed, but is Exodus made up out of while cloth? And when?
/u/eclo provides a discussion of specific attempts to address the Exodus story. At the same time, the field of folklore provides research on how people end up creating, repeating, modifying, and believing the stories that they tell. The birth of a legend - a story told to be believed - does not take long, and it can seem ancient in short order.
The following is an excerpt from my Introduction to Folklore that addresses the problem as it was addressed when trying to chase down the origins of recent Urban Legends:
The answer to [the question about the origin of legends and folktales] is somewhere between "we don't know" and "it's just what people do" – that is, they invent these sorts of stories. Several folklorists, including the late Alan Dundes and Jan Harold Brunvand, recognized an opportunity with recent urban legends to finally track down "the source," the point of creation, to better understand how stories originate. For the most part, they were unable to find the point/person of origin to any general degree of satisfaction. It is a maddening question, and much like the proverbial chicken and the egg, it isn't likely to be resolved.
People tell stories. People repeat stories. And as they repeat them, people modify stories, which sometimes results in the birth of new stories. There might have been some highly imaginative, creative people who invented stories at some point, but that sort of person has yet to be identified in the annals of folklore studies. Folklorists often asked renowned storytellers to tell a new story, to invent something that they had not heard. Without exception, these requests were refused by the storytellers who explained that while they repeated stories, they did not invent them. In general, it may be best to consider the possibility that the process of repetition and transmission is the source of much of the creativity that is evidenced in the international library of oral tradition.
One example may help shed light on the creative process: the Cornish droll tellers were known for their wild adaptation of the material they heard. Their counterparts in Ireland were the seanchaithe, professional storytellers who prided themselves in the faithful recitation of stories they had heard, as close to the original as possible. Perhaps in this, we can see the opportunity for new stories to be born, and indeed, Cornish oral tradition includes more than its fair share of distinct subtypes (i.e. variants) of legends and folktales, perhaps offering a hint as to how these things may come into existence.
'The Bible Unearthed' by Finklestein and Silberman is a good introductory book on the archaeological evidence behind the bible. It's for a general audience and written by respected archaeologists, it should be easily available. I think there's a tv documentary too. I'll try to recall what we covered in biblical archaeology but I am far from an expert! The general consensus in archaeology is it's a myth based on cultural memory and oral histories - there is evidence the 'Israelites' as we know them now (there's disagreement over the name too afaik) were in Egypt and did travel over Canaan but not in the way the exodus portrays. Basically there is no scholarly consensus on the issue and it gets much more complicated when you add religion in. The view I tend to agree with is that these memories became mythologised and this myth was solidified in a political and religious attempt to create unity and legitimacy as a people and as a people with a right to reside there. At the time the levant was caught between competing empires such as Egypt, Babylon and the Hittites, and the Canaanites/Israelites got stuck in the middle, so it is understandable such a story developed and was included in the 'canon'. I don't believe someone just decided to make up the story one day but that it developed over hundreds of years from oral histories, which would often be embellished and attain 'mythical' status. It's a complicated issue, especially as people have, and still do to a lesser extent, tried to use archaeology to 'prove' the bible. 'Archaeology of the land of the bible' is a good book too (in two volumes), but more academic so I'm not sure how easily available it would be.