Well said, Nick.
I would suggest that anyone who’s interested in this start out by reading Diarmaid Macculloch’s History of Christianity – an excellent book written by a preeminent historian. In summary, there are plenty of things in the Bible which are well-evidenced, but the Christmas story is unfortunately not one of them.
Unfortunately for Matthew, the Romans were highly efficient at keeping records and distributing them widely across the Empire. The idea that Caesar Augustus might have decided to tax the whole world and then destroyed all trace of the paperwork is almost as laughable as the idea that he was remotely interested in Joseph’s ancestry in Bethlehem. So, it’s probably best to take that star with a pinch of salt.