* Palestine existed in 10,000 BC and was occupied by the
Phoenicians, Babylonians, Greeks, Romans, Byzantines;
among several.
No, 'Palestine' did not exist until after it was a Roman Protectorate. It was thus dubbed in retaliation for Jewish uprisings, renaming the land 'Palestine' after the previous (to the Jews) Philistines. Prior to that it was Judea, Samaria, and Phillistia in various portions, and before that it was Canaan.
* Edited to add: Partly Edom/Idumea, parts of Moab, Midian variously.
** Edited to add: And of course, Israel, however briefly.