No Oralloy, there is zero evidence of this outside of the mythological text.
The fact that Egyptian hieroglyphics have a mythological component to them has not prevented historians from using them to reconstruct a history of what happened in Egypt and the surrounding region. In fact, the ancient written records of almost any nation have quite a bit of mythology intertwined in them. Historians still use them to determine what happened in a nation's past.
Non-religious scholars, that would include scholars from Israel, all accept that this did not happen.
All scholars agree that Egyptian records show that the Hebrew deity was a local deity in the area where desert nomads roamed.
All scholars also agree that textual analysis shows that the lines about the slaves escaping across the Red Sea are the oldest part of the Hebrew bible.
All scholars also agree that Egyptian records show that the Israelite culture existed at the very beginning of the Iron Age (1200 BC).
Now, it might be hypothetically possible for Judaism to have reached Israel by other means. Perhaps aliens came in UFOs and transported people back and forth between Jerusalem and that mountain in the desert.
Occam's Razor though suggests that it might be a bit more plausible that the Hebrew accounts of escaped slaves passing by that mountain on their way home might be the way it happened.
It is a myth. It is the same as Noah's ark. Some people really really want it to be true, but it isn't.
The historical evidence says otherwise.