As it turns out, Luke did know what he was talking about. Assuming that it is true that Jesus was born while Herod was still alive (Matthew also says as much), we can see that the census of AD 6 under Quirinus cannot be the one mentioned in Luke 2. So why does Luke bother to mention Quirinius? It turns out that the Greek word prote, in Luke 2:” can mean either “first” or “before.” Translators—without consulting the historical context—usually choose the most common meaning, “first,” and end up with the phrase as it’s usually translated. However, in this case, it should be translated “before,” so that the verse should be translated, “this census was before Quirinius was governing Syria.” Luke’s point would then be to distinguish the census that was taken around the time of Jesus’ birth from the more famous one that caused an uprising in AD 6. In other words, Luke is saying that Joseph and Mary had to travel to Bethlehem because of a census, but he’s clarifying, as if to say: “Do you remember that big Census we had with Quirnius became governor of Syria? Well, it’s not that one—it was before that.”
At the time of Jesus’ birth—when Herod was still alive and King of Judea—the proconsul of Syria was one Sentius Saturninus, who held the office from 9 to 5 BC. Tertullian knew this, and mentions a census conducted by Saturninus on behalf of the emperor in the year 6 BC. Although the logistics of a census requiring the kind of travel that we read was forced on Joseph and Mary is unclear, whatever compelled them to go to Bethlehem could not have been the census ordered by Quirinius but must have been a census taken at least ten years earlier. And although there are no extant Roman records of the specific census in question, we know that such enrollments were ordered at the time. All this is to say that if New Testament translators would check their history, they would know how to translate Luke 2:2 correctly. And they would know that Luke did know that he was talking about, and his witness can be trusted with regard to dates. (James L. Papandrea, Reading the Church Fathers: A History of the Early Church and the Development of Doctrine [Manchester, N.H.: Sophia Institute Press, 2022], 200-1)