We are told that some Jews went to Egypt after the murder of Gedaliah (2 K 25:26). We know for certain that there were Jews at Elephantine over a century later -- their correspondence archive has been found.
Arachnophilia writes:
the date i have in mind is around 600 bc.
The Babylonians had already started flattening the Jerusalemites. Maybe some decades earlier, when Jerusalem had a high point under Manasseh and then Josiah.
I tend to think that the exodus tradition is post-exilic, which should mean that Genesis is as well. There was racial tension between native Egyptians and the Jews in Elephantine and probably wherever the Jews lived in Egypt for the sacrifice of the ram was important in Jewish cultic practice, while the Egyptians had a goat headed god, Khnum, so there was bound to be strife.
The material that Josephus records in Contra Apion is of Egyptian literature which packages the Jews in the image of the hated Hyksos with interesting twists such as the leader of the Jews was an ex-priest of Heliopolis called Osarsyph who changed his name to Moses, or that the escaping group all had a disease. Pretty contemptible stuff aimed squarely at the Jews. I think the Jews in Egypt accepted the notion that they'd been in Egypt before and sanatized the Egyptian polemic giving virth to a Jewish version which was the basis of the exodus.
Of course one needs an exodus to have a Joseph sojourn in Egypt. Some of the other Genesis traditions are probably earlier. Jacob may be quite early as compared to Abraham who gets a lot less press and is not represented much at all in the prophets, whereas Jacob is ever present.