Historical basis for the Exodus

[Statilius the Epicurean]

Dunno what you mean. On a secular level there's no reason to assume that archaeology must be reconciled with the Biblical narrative, so it's not like we need a secular explanation. The lack of archaeological data for the Exodus is only a problem for literalists.

I don't think we can confidently say anything about the Exodus in historical terms other than there was a tradition of Israel being brought out of Egypt by Yahweh, it was possibly quite early (Song of the Sea and the Book of Hosea), and whatever tradition existed was expanded by later authors.