Is there any historical evidence whatsoever to suggest that real events inspired the Passover story, where Moses led his people out of Egypt?

by clean-yes-germ-no
Flubb

No. There's two camps that say why - one says that we haven't found the evidence (yet, or perhaps it's obfuscated (there are good reasons)), the other says there's nothing to find because it's a tradition made up/fabricated at a later date (normally the Babylonian Exile), so stop looking.

The Passover is very important however, and the Biblical text preserves the fact that the Passover is the beginning of the new year for the (recently) released Israelites. The Egyptian calender is a solar one but this new Israelite one is lunisolar. All 4 liturgical calendars in the Old Testament (2 in Exodus, 1 in Leviticus, and 1 in Deuteronomy) all start with the Passover. While the Exilic Israelites ended up using the Babylonian names for months, the earlier calendars didn't - and there are only 4 months from this calendar that we know the names of ('Aviv, Ziv, 'Ethanim' and Bul), which happen to coincide with the equinoxes. Passover starts in 'Aviv, and while there are other feasts in other nations at this time (spring), the reasons for the Israelite one are unique - the escape from Egypt.

The problem with the Exodus is that while the events and details are very difficult to corroborate, the fact that Israel came out of Egypt runs throughout the Old Testament. This doesn't mean that it happened or is true, but if we're going down Occam's route, then it might simply be that. I'd suggest that the Passover might be one such indicator- it's not direct evidence by any means, but it is a suggestive ancient echo.