Did the Exodus from Egypt to Canaan actually happen? If so, how did the people who became known as "Israelites" cross the Sinai without leaving any evidence behind them?

 

Yes, the Exodus did occur. It happened ~1265 BC the year that Amun-her-Khepshef (heir to Ramesses II) died. The Bible is unclear as to how many people actually left in the Exodus as in Hebrew, the word for thousand can also mean clan.

What evidence (I assume you mean physical) do you think a group would leave behind if they were just passing through an area 3300 years ago? Especially when we aren’t certain of their route.

Here is some of the evidence for the Exodus:

1. Amun-her-khepshef’s death and the abandonment of Avaris in the 1260’s BC.
2. The Merneptah Stele dated to 1208 BC. It is the first time we have evidence of the name “Israel.”
3. The Mt Ebal Altar dated to ~1220 BC also called the Joshua’s Altar. It only has remains of sacrificed kosher animals.
4. Population explosion in Canaan ~1220 BC.
5. Merneptah was unable to keep the Libyans from getting to the Nile until the Battle of Perire (1208 BC). This would never have happened under Ramesses II. Losing a single chariot was really bad. Losing a division of chariots was catastrophic as not only have you lost chariots, but you’ve lost the crews and thus, the institutional knowledge.
6. Jericho and Hazor have evidence of being destroyed by fire in the 13th Century BC as the Bible indicates. Ai, the other city destroyed by Joshua in the Bible, has not been definitively found. No other cities were burned in this way according to the Bible or archaeology.
7. An Akkadian to Amorite guide book has been found in Iraq. We now know that Amorite is the parent language to Hebrew, and they are as similar to each other as Australian and American English. This gives evidence of a Hebrew type language dating to 1800 BC not 1000 BC as previously thought.
8. The Torah/Pentateuch has many more Egyptian New Kingdom place names and loan words. There are no Persian loan words as would be expected if it were written during the Babylonian Exile.
9. The Ark of the Covenant is designed in the same way Egyptian ritual furniture is.
10. Ugarit and Egypt used ideal numbers for the dedication of their temples for theological messaging. This gives precedent for the 480 years in 1 Kings 6:1 being symbolic rather than literal.

The idea that there is no evidence for the Exodus is just plain laughable.