This is a question that has been a point of controversy among biblical scholars and skeptics for centuries. History tells us that Caesar Augustus reigned over the Roman Empire from 27 BC to AD 14 and ordered a census to be conducted during his tenure. Herod the Great reigned until 4 BC, meaning Jesus has to be born sometime before that time. The mention of Quirinius as governor of Syria in Luke chapter 2 appears to cause a problem as history records that Quirinius held this office between AD 6-7, at least 10 years after the birth of Jesus according to Matthew and Luke. There are at least three possibilities here for how we can interpret what is written in Luke 2:2:
(1) Luke made a historical error. This would presuppose that Luke was not inspired by the Holy Spirit in all his writings.
(2) The Greek word for “first” in Luke 2:2 is protos and can be translated “before.” Thus Luke 2:2 could actually be translated, “This was the census taken before Quirinius was governor of Syria.”
(3) Quirinius actually ruled Syria on two separate occasions and there were actually two censuses taken. The “first census” mentioned in Luke 2:2 occurred during his first term as governor, and another was ordered during his second term as governor mentioned in Acts 5:37, which probably took place between AD 6-7 (Josephus links this census to an uprising under Judas of Galilee). 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.
Further, the Christian doctrine of the inerrancy of the Word of God (2 Timothy 3:16, 2 Peter 1:20-21) leads us to accept explanation (2) or (3) as the most likely, with the most evidence pointing to explanation (3). The Bible is true and spoken from God’s mouth (God-breathed), and we accept it as truth more than the historical writings of the Romans or even the writings of the Jewish historian Josephus.