In a Passover article for the Jerusalem Post, Stephen Rosenberg searches for indirect evidence connecting the Israelites to Egypt.  He finds some significant connections:

The Torah is full of references to Egyptian geography and religious cults and customs, and it is clear that the compiler was speaking to an audience familiar with Egypt. When Lot parted from Abraham, he chose the plain of the Jordan because “it was well watered… like the Land of Egypt” (Genesis 13:10). The Tower of Babel in Mesopotamia was built of brick, because “they used brick for stone” (Gen. 11:3), it being necessary to explain this to the Israelites, who only knew monuments built of stone, as in Egypt.
[…]
With reference to temples, one can see that the description of the Tabernacle of the Wilderness, the Mishkan, is based on Egyptian models. The Ark of the Covenant is made of three layers, a wooden chest overlaid with gold inside and outside, like the sarcophagus of Tutankhamun. It is protected by two cherubim, just like that of Tutankhamun, except that he had four. Much of the furniture from his tomb was fitted with carrying staves, like those of the Tabernacle.

But then he goes further and suggests that the Israelite tabernacle was in fact the battle tent of King Tutankhamun, stolen by the escaping slaves.  That leads him to propose a 14th-century date for the exodus.

In that case Akhenaten, who had started his reign under the official name of Amenhotep IV (1350-1334 BCE), was the persecutor of the Israelites, “the Pharaoh who knew not Joseph” (Exodus 1:8). He was the one who ordered the male babies to be drowned, from which fate Moses was saved to become a prince at his court, as Sigmund Freud suggested 80 years ago. When Moses saw his brothers slaving at the building of the city, he reacted as described in the Torah and eventually, on the death of Akhenaten, saw a chance to lead them out of Egypt.

The “suspicious circumstances” of the deaths of both Akhenaten and Tutankhamun later “perhaps gave rise to the idea of the slaying of the firstborn.”  Rosenberg seems serious when he suggests that the story of the tenth plague originated from the life of Akhenaten who “had six daughters and two sons who seem to have died young.”  I wonder if there was a single Pharaoh who did not have some children die young, and I doubt that the Israelites required such an occurrence to prompt them to make up such a story.

Rosenberg then proceeds to propose a chronology, but since he refuses “to take the biblical figures at face value,” he must admit that “all this playing with figures is speculative.”

He concludes:

Sitting around the Seder table we like to believe the full biblical account of the Exodus, the 12 brothers, the slavery, the Ten Plagues, the national release and the gaining of our freedom. The historians and archeologists think it is all a wonderful folk-tale but hardly one founded on any historical fact. Proof there is none, but information based on equating the battle tent of Tutankhamun with the Tabernacle of the Wilderness can, when put together as above, make a credible narrative.

I doubt the anti-supernaturalist historians find this approach credible, and I certainly prefer to accept the biblical account over the latest attempt to create a new story by admitting certain evidence and excluding the rest.  Nevertheless, I appreciate Rosenberg’s presentation of data that may be understood in several different ways.