Josephus (Jewish-born, Roman citizen historian who lived through this period) makes no reference to a 'star'. He does mention Pilate and James, brother of Jesus. He calls Jesus 'a wise teacher', but anything written then (including the epistles, etc. that became the Bible) had to be re-written periodically as paper/parchment/vellum wore out, so it's not clear if that's a later insert. But... NO mention of a new star in the sky. If he had, I wouldn't find that conclusive (that pesky re-write issue) but... he didn't.

There was little/no artificial light (so no light pollution and people under the night sky would tend to have dark-adapted vision. I would think that a new bright celestial object would both be noticeable and certainly mentionable, especially if you were writing about Jewish antiquities.