I have wonder whether we really know one way or the other.
As far as I know, we have not been given this information either in the Bible or in contemporaneous non-Scriptural sources. A case can be made for either contention, as well as for a variety of other factual assertions about Jesus’s life, using Scripture, information about Jewish belief and practice, and archaeological information.
However, “making a case” and “proving” are two very different things.