Luke sets the birth of Jesus in a specific time and place. He begins with the time. Caesar Augustus is the Roman emperor. We know from Roman history when that took place. Quirinius had two appointments as governor of Syria. Both men are reported on in the history of Rome.
Isn't it amazing how God can use the most powerful person in the world to do His will. Caesar Augustus was certainly the most powerful person of his time. He wants to get an accurate count of the population of people in his empire to know how to tax them. God wants to move Mary and her unborn baby Jesus from Nazareth to Bethlehem, the city of David, so Jesus will be born there. Caesar's order got the job done.
God was working things out according to His plan. As the Apostle Paul tells us in Galatians 4:4-5, "But when the right time came, God sent his Son, born of a woman, subject to the law. God sent him to buy freedom for us who were slaves to the law, so that he could adopt us as his very own children."
He is working in our lives right now, even if we can't see it or don't recognize it. We can count on God to always keep His promises.