I hate internet religious discussions and have sworn them off. However, the known facts are seriously reasonable and perfectly compelling to the point that I choose to believe it as if there was an extant Roman or Judean Certificate of Live Birth, notarized.
I'm hoping your'e not interested though. It would take a lot of typing that I don't want to do and in the end, I don't care to convince anyone of anything anyway. Additionally - and ironically - at this point his date of birth has more to do with the future than it does with the past. That's why some of the events surrounding the Nativity are mentioned in Revelation which is a prophetic book.