Well, we do have some letters from Simon bar Kokhba from his revolt in 132 CE. Unfortunately, he holed up in Betar, which was destroyed by the Romans (who, per Jewish tradition/sources, killed everyone in the fortress save one witness). The letters have been found relatively recently, and new discoveries are found in Israel reasonably often, so it's possible that more documents may some day be unearthed.

Unfortunately, Jewish Messiahs other than Jesus tended to lead revolts, and the Roman response to having legions destroyed got more and more extreme with each uprising. And that's on top of the fact we have a very small percentage of all written records from before the age of the printing press, for various reasons.