First of all, there are fundamentalist who believe absolutely in the Biblical account of the Exodus as direct revelation from God to Moses. In the more scientific and historical schools of study, even without the above literalism, the Biblical account is sufficient as the basis for both a legal system and faith system.
Could one remain a faithful servant of God and also accept the possibility that Moses, as described in the Torah, may be as much legend as historical - perhaps more legendary. It's hard not to consider this as a theoretical possibility if only because of the existence of very responsible and academically sound schools of Biblical studies (Harvard), that suggest that the books of the Bible from the time of Genesis through the time of King David were redacted by David's court historian.
"Evidence" is a complicated term. I don't know of any scientific proof of Moses. However, if the "Habiru" mentioned in some historical records are in fact the Hebrews, the children of Israel, then there is some historical evidence.
If the Hebrews lived in Goshen or thereabouts, they would have been using Egyptian materials, equipment, etc., thus it would be difficult to prove a different people lived in Egypt. Furthermore, if there were evidence, I would expect a reluctance on the part of the Egyptians to offer opportunities for Jews to look for evidence of their existence in Egypt and their successful exodus.
Thanks to Rabbi Dov.