Palestine has existed for thousands of years, going back to the time of the Egyptians before Christ. The city of Gaza today was the land of the Philistines. The Greek historian Herodotus identified the Holy Land as Philistina. The Romans after defeating the Jewish uprising under Bar Kokhba, identified the Holy Land as Palestine-Syria.
Whatever the people called themselves is irrelevant. Using the word "Palestinian" or not, they were the natives of the land, living there for generations. Genetic tests have even proved that these Palestinian "Arabs" are the natives of the Holy Land. Israeli scientists and rabbis actually admit this: