After they were conquered. Nobody spoke Arabic before the Islamic conquest destroyed their language, culture, and ancestral religion.

Fun fact: Some Palestinians still follow old Jewish customs to this day.

There are still groups of not fully Arabized peoples all over the Levant, that managed to preserve their heritage. Arameans, Samaritans, Druze, Assyrians, Copts, Armenians, Maronites, Greeks, Yazidis, and others.

Palestinians are a mix of local Jews that converted to Christianity, later Islam, Greeks, Arabs, Egyptians, Africans, Europeans, Syrians. During the early 20th century, when Jews immigrated, lots of Arabs came from neighboring countries as well. Al-Masri (the Egyptian) is the third most common surname among Palestinians for a reason.

This study from 2012 is the best DNA genealogical analysis, I know of.

According to historical records part, or perhaps the majority, of the Muslim Arabs in this country descended from local inhabitants, mainly Christians and Jews, who had converted after the Islamic conquest in the seventh century AD (Shaban 1971; Mc Graw Donner 1981). These local inhabitants, in turn, were descendants of the core population that had lived in the area for several centuries, some even since prehistorical times (Gil 1992)... Thus, our findings are in good agreement with the historical record...

Jews and Palestinians are practically cousins.