It’s a fair assumption that of the two witnesses to early Israelite history, the Hebrew Bible and excavated artifacts, the latter should be the starting point for reconstructing Israel’s past since a text preserved by copying is, after all, significantly more fluid than artifacts preserved in the ground. Burnished, red-slip pithoi in Early Bronze II at Tel Halif don’t lie (not that I know what they say), and this is before you get to the question of the historicity of the original writings.
So then starting with archeology, the theory of origins farthest from the traditional says that Israel was a confederation of tribes native to Canaan. This thesis begins with the paucity of remains in the relevant strata in the Cisjordan that indicate a hostile takeover, as recorded in Joshua, and the similarity in material culture among different sites in Palestine, making Israel essentially indistinguishable from Canaan. The city-state milieu of the Levant and the parallels this kind of confederation has with, say, the Philistine cities of the coast certainly commend this view. As any good materialistic explanation, it precludes anything miraculous, and so the biblical account must be re-examined and stripped of mythic elements and theological redaction. Once this is done, the left-over kernel should be more or less historical, or at least more amendable to the archaeological data.
Then to what extent can the received text be de-mythologized? Of course we could take out anything supernatural (no plagues, no Red Sea crossing) and most characters could be dismissed as legend (no Abraham, no Moses). But however virulently we wield our skepticism, we cannot take out the core story of a non-native people leaving Egypt to reside in Palestine—because no one would have made that up. Whatever the nature of an ancient peoples mythology, what is never claimed is any kind of inferiority and anything less than utter entitlement to their land.
It seems nearly unimaginable that a civilization would create a myth around an ancestry of slavery to a neighboring people and a wandering in the Sinai for lack of courage. Counter-intuitively, in the Hebrew Bible we do not find a mythology wherein the Israelites define themselves as special progeny of the gods, but a people who consider themselves entirely ordinary, privileged only because Yahweh became the patron of their ancestor—who came, incidentally, not out of the sky or the sea, but from Sumer.
This is very odd, and I think quite a problem for those who want to do away with Exodus entirely. However you deal with the specific elements of the mythology of Israel, the core of the narrative includes an exodus and so there must be an eisodus. Archaeological interpretations that do not take into account even a minimalist version of the text can be discounted.
____________________
See Dever, Who Were the Ancient Israelites…, and Mazar, Archaeology of the Land of the Bible