Jews "left" Judea/Israel (and I use those terms because Palestine was a name not given until much later, often attributed to the Romans as they called it Syria Palaestina after conquering it), is the usual narrative assumed to be true from Biblical times. There are stories of expulsions by the Romans and the Babylonians and other conquerers. However, this doesn't seem to line up with what historians have found. Many believe that instead, Jews actually converted (often to Islam) and remained in place. This would be easier than paying the jizya in Muslim society (tax on non-Muslims, sometimes required because non-Jews didn't serve in military drafts, i.e. in the Ottoman Empire as I've understood it), and generally easier than being a minority. Jews either converted or sometimes were killed/expelled in various wars as well, but it's clear that some stayed.

There is no evidence of a major migration out of the region in the 1st Century CE, but there were changes in where the population lived by area and there were shifts in the religious preferences of those populations based on who was in control, from time to time.