I have been interested in the potential for kernels of historical truth in the Bible / Old Testament for some time. In regards to the story of the Exodus, I have seen evidence that points to a memory from the Canaanite ancestors of the Kingdom of Judah. In https://books.google.com/books?id=UEWWCwAAQBAJ&pg=PA230#v=onepage&q&f=false the author claims that Senusret III made campaigns into the Levant as far as Schechem.

Additionally, I have seen claims that the story of the Exodus is actually a “reversed” story of the Hyksos (Israel Finkelstein entertains such a claim in his work “The Bible Unearthed”). Evidence for this comes from the Hyksos seeming to originate in the Levant, rule from the eastern delta area and eventually are chased out of Egypt by the founder of the 18th Dynasty.

In a similar vein, some suggest that perhaps the character of Moses is based on the Pharaoh Akhenaten and his “attempts at monotheism” though this seems less likely to me, because I’m unsure of how a Judean populace would come to know of Akhenaten’s reforms. I am familiar with the Amarna letters, but would the “average” Judean have been familiar with their content? Would he even have heard of Akhenaten, let alone heard of his religious reforms?

Others have suggested that Ramses II is the Pharaoh of the Exodus story. There is his well known campaign into Kadesh Barnes so it seems likely that he had campaigns in the Judea / Israel area as well. Additionally, the Bible mentions the word “Pharaoh” and it is my understanding that Pharaoh comes from “Pa-Ra-Me-Su” the same root as “Ra-Me-Su” and that the title of Pharaoh itself was adopted as a reference by later rulers to the greatness of Ramses II’s reign.

However, all the above rulers lived significantly before we have any evidence of a Kingdom of Israel or a Kingdom of Judah existing - let alone a hypothetical United Monarchy.

The Book of Kings mentions Pharaoh Shoshenq I, do it is possible the Exodus story was constructed around this time “to deal with” current events surrounding Shoshenq I’s campaigns.

Additionally, I believe Necho II is mentioned in Jeremiah.

Of the aforementioned Pharaohs, did any of them influence the Exodus story. Perhaps a historical memory involving multiple Pharaohs was actually at work? Perhaps the Exodus story was written around the time of the Babylonian invasion and “deals with” those events through the allegory of a Pharaoh? Clearly the solution to this is dependent upon when one believes the Exodus story was written, but how long do historians suspect it existed in oral form before being written down? I realize this is a long question so thank you for those who take the time to read it.