That's like saying Cornwall was part of the British Empire, so doesn't really exist.
Palestine was a recognized area, with a population calling themselves Palestinian.
The term "Palestine" has been used for millennia to refer to a geographical region in the Middle East, with changing borders and political entities over time. The name itself derives from "Philistia," referring to the Philistines who inhabited parts of the southern coast. The Romans later revived the name in "Syria Palaestina." After the fall of the Ottoman Empire in World War I, the area broadly defined as Palestine (between the Mediterranean Sea and the Jordan River) was placed under British administration as the British Mandate for Palestine (1920-1948). During this period, it was a recognized administrative and geographic entity.
Throughout the British Mandate period and certainly before, the Arab population residing in this geographic area developed a distinct identity and increasingly referred to themselves as "Palestinians." This identity was tied to the land and their shared cultural and historical experience within it.
That's history for you