Christianized Jews and Jews generally were spread throughout and beyond the empire. The persecutions, even postwar, were terrible but relatively localized and there is no reason to believe it involved the mass redaction of all existing documents (not even possible!) and then-unwritten oral histories (which then everyone, antisemites, Christians, pagans, all alike decided to maintain silence about even though they would have been delighted to show their enemies up with this evidence) except that it makes people feel clever to think so.
Even more incredibly, plenty of heretical documents did survive! People were one hundred percent successful absolutely crushing any leaks of a vast conspiracy to “justify the status quo” (why do you even think it needed justifying?) even against powerful groups that would not have wanted to…but couldn’t stop eg the Gnostics.
Most scholars don’t think that about the Old Testament either, although I have been learning lately it is very much in vogue on certain corners of the Internet. But at least that is in some respects at certain times more plausible depending on the specific text and time period being talked about, if very early. The Christianity conspiracy theories really aren’t. There’s no evidence for them whatever and yours in particular boggles belief, and is really not remotely feasible. This is basically the zeitgeist nonsense with a different spin.