Some dumb rabbi in the middle ages said that Rebecca in the Old Testament was 3 years old when she married Isaac. But in Genesis 24 we see that she is a young woman able to do chores and give her own willful consent.
I also had a Dutch missionary colleague defend tribal child marriage by using Mary's supposed young age. But I see no evidence that Mary had to be 14 or 15 years of age. Just because some Jewish families arranged marriages that young does not mean Mary's family did. I see no evidence whatsoever about her age, except that she was a young lady.
Roman tax law: I think in Roman law the tax was paid after age 18 and Mary and Joseph were on their way to pay the tax. But I don't know if that was due to Joseph's age or to Mary's. If both, this means that both were over 18 if my info on the Roman taxes is correct.
People love to speculate on the supposed young age of biblical characters. I heard a youth pastor once argue that, with the exception of Peter, all of the 12 disciples were teenagers. Of course there is no good evidence for these assertions, other than they seem to fit whatever narrative the person making them is trying to push.
Considering Mary had the apparent autonomy to suddenly take off (perhaps not on her own, but seemingly of her own volition) and visit her relative, Elizabeth, would suggest to me she was older than an early teenager.
Her mature response of praise recorded in Luke 1:46-55 would also be exceptional for a 14 yr old.