Aye, I have a problem with that Census, Luke gets it mixed up, it was for Jesus' Bar-Mitzvah. OK, adjust the "not", sorry.
In Y0 Quirinius was Nero's tutor in Rome, and he didn't arrive in Judea until after Archelaus was fired for incompetence and Rome imposed direct rule: it needed to know what it was supposed to be running. If Jesus was born in Herod the Great's time, then he was born before Herod's death in 4BCE. The best guess is 7BCE, making Jesus 13 in 6AD/CE, the year of the census. We know he was presented for his Bar-Mitzvah at the Temple, and that his father could not go there while the Herodians were on the throne, being a rival claimant to the throne.