Such a decree does not reflect ignorance on the emperor's part, but arrogance. Luke 2:2 This was the first census taken while Quirinius was governor of Syria. (When Critics Ask) Gotquestions asks "Does Luke’s Claim that Jesus Was Born in Bethlehem at the Time of Quirinius’ Census Match the Historical Record?As great as the Roman empire was, he certainly knew that Rome could not gather taxes beyond its own boundaries. The KJV translates it "(And this taxing was first made when Cyrenius was governor of Syria.)" Luke's Gospel is not only good news but it is a historically accurate record of the events surrounding the birth, life and death of the Messiah. " This is a question that has been a point of controversy among biblical scholars and skeptics for centuries.
With Luke being the author of both Luke and Acts and wanting to write in “consecutive order” (Luke 1:3), it would seem unlikely for Luke to make such a mistake in dating.
(See Gotquestions an excellent resource) What Year Was Jesus Christ Born? More specifically, Jesus would have been approximately 32 years old at the time He began His ministry (still “about thirty years of age”). The tradition of December 25 was developed long after the New Testament period.
The Bible does not provide the exact day or even the exact year in which Jesus was born in Bethlehem. It’s the day Christians have agreed to celebrate the birth of Jesus, but the exact day of His birth is unknown.
He reckons not events according to their apparent importance; the standard of the sanctuary is a very different measure from that which worldlings use. Roman civilization had brought peace and a road system (2).
When any purpose of God is to be accomplished, all other things will be subordinated to it. Grecian civilization provided a language--the lingua franca (3).