Tacitus wrote around AD 116, roughly 80 years after the crucifixion. Isn’t this just secondhand hearsay?

Tacitus is writing decades later, and he was not present at the events himself. As a Roman senator with access to the empire’s own administrative and judicial records, though, he is exactly the kind of source who could check a claim like this if he doubted it, and he had no reason to invent a Jewish provincial’s execution just to make his own point about Nero and the fire of Rome.

The value of this source isn’t that it’s proof on its own, but that it comes from a hostile, non-Christian writer and lines up with what the earliest Christian sources already said. Independent lines converging on the same bare fact, from friendly and unfriendly witnesses alike, is what historians look for.