Does it matter?
Back then, history was written by learned people about famous people. No one cared what happened to a simple carpenter and his wife, at least until later...a lot of that happens with history, it's going on, and people react to it rather than record it.
It took over 500 years to get Easter figured out, and they had some major knockdown dragouts about that (the Venable Bede talked of little else, if you go by documentation...
You have a Jewish offshoot religion that suddenly welcomes Gentiles (thanks, Paul..., and underground movment, a religion of slaves, and eventually an official Roman Imperial religion. Several books of the New Testament (the Apocrypha) were 'tossed out', not to mention Gnostic gospels, etc....
Even the Quran was memorized for several decades, until a codified version could be put together. Even so, there's a body of works (I think it's called the Hadith) that might be parts of what, when and where
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anahl nathrak, uth vas bethude, doth yel dyenvey...