They are a specific people with a unique culture apart from the other Arabs. Palestine is the levant not the peninsula. This is where you are wrong. There has always been the Palestinian nation. You keep looking for European-centric definitions. The world is not Europe-centric. Amongst the people (Arabs, Persians, Turks) there has always been the Palestinians.
Before 1948 there was serious consideration to be part of a greater Syria. That didn’t work out (due to European imperialism) so they focused on being Palestine independently. That didn’t work out because the European Jews who worked directly with the European imperialists used their connections to steal Palestine.