Clear usage, yes, but similar names were known since much earlier. Egyptians in the 12th century BCE refered to a neighboring people (and/or their territory) as "Peleset". The Assyrians called the region "Palashtu" in the 8th century BCE. The Old Testament talks a lot about a close neighbor called "Philistines", with whom the Israelites are said to have fought many wars. So it seems safe to assume that Palestine has been a thing since a long time ago, and that its boundaries fluctuated depending on the political and economic fortunes of various ethnic groups.
Those dates are still well after the Exodus. And Philistines, Palashtu, Peleset are not the same as Palestine which was the name used in R_haterade's comment.
The Israelite exodus was from from Egypt to Canaan, not to "Palestine".
Sure, and no Indians ever lived in America before white people arrived because the land wasn't called "America" and its inhabitants weren't called "Indians" back then.
Does it really matter whether the Israelites migrated to Canaan or Palestine or Judea or 31°47′N 35°13′E or whatever as long as we all know roughly which part of the world we're talking about?
Yes. Yes historical accuracy matters! (Wars have literally been fought over the correct name and owner of this land, and launched with the false belief that what we call, "Palestine" today existed before Israel existed. This simply is not true.)
https://en.wikipedia.org/wiki/Timeline_of_the_name_%22Palest...