In the swirling debates about the historical Jesus one of the peculiar things about the gospel of Jesus is that the tellers of the gospel versions brought so many OT prophecies into the story. Some sceptics have proposed that the writers knew these prophecies, were committed to their fulfilment, and accordingly bent the facts about Jesus to fit with the prophecies (sometimes called 'prophecy historicised'). But in Advent, when some of these prophecies are read, we might pause and reflect on what those prophecies were principally focused on. In sum, they were focused on a new Davidic king and created an expectation of a new king of Israel coming (see, e.g. Matthew 2:2, which connects back to, at least, Jeremiah 23:5, "I will rise up for David a righteous Branch and he shall reign as king.")
In the context of Israel under the thumb of Herod (not wholly Jewish, in character not ruling as a Davidic king), himself a client of the Roman emperor (absolutely Gentile, not Davidic), this expectation could only have been of a politico-military ruler who, by implication, overthrew any other rulers over Israel.
That makes it all the more striking that the life of Jesus when told as a narrative, initially in oral stories, then in written documents, drew into the telling OT prophecies about someone who would do what Jesus did not do: he did not become a politico-military ruler and he did not overthrow either Herod or Caesar.
What on earth led to this person who wielded neither sword nor sceptre being proclaimed as the one who precisely fulfilled the OT prophecies? Here the sceptics are in some trouble. Without the miracles in which Jesus established himself as a different kind of ruler (over nature, over sickness, over demons, over death) actually happening, it stretches credulity to think that a mere rabbi generated belief that this man was not only a great Teacher but also a great King.
But if the miracles as told did take place we have some credible reasons for understanding why the followers of Jesus thought he fulfilled the prophecies of their Scriptures. Beyond a sense of 'tricks' performed by Jesus as an ancient magician, something happened which transformed the understanding of these prophecies so they applied to this (so to speak) non-king who was King. On the one hand the resurrection of Jesus on this analysis was the clincher, and the event of the resurrection must have been more than an inner sense of joy transforming the grief of the disciples at the loss of their rabbinical leader. On the other hand, thinking about Christmas, it is likely that the story of Jesus was fuller than the one told by Mark, in which Jesus arrives on the scene, an adult with the barest of preparation heralding his arrival as the non-king who was King.
True, the birth narratives told by Matthew and Luke raise many questions: do their differences betray a lack of real knowledge about Jesus' birth and infancy so that for this part of Jesus' life, prophecy was being historicised? Yet both narratives agree on significant details (names of mother, putative father, Bethlehem as birthplace, Nazareth as place of upbringing, special conception). Neither feels compelled to tell their respective birth story as a definitive royal story. Matthew concentrates on Jesus being born as a rival king to Herod while Luke's attention to dates and census places Jesus as a rival king to the emperor himself. Were they madly inventing this part of Jesus' life to suit the conclusion reached by the early Christians after his resurrection? It makes sense, I suggest, to think that the conclusion reached had its antecedents before Jesus' might works as an adult: from the beginning of his life, indeed before the beginning, there were signs of God doing a great thing. Both Mary (according to Luke) and Joseph (according to Matthew) are prepared for the unexpected pregnancy as well as the unexpected life Jesus will lead. An extraordinary adult life has extraordinary preparation and development through infancy and youth.
All in the above paragraph is harder to 'prove' than the adult activities of Jesus, even among those of us who have faith in Jesus. The early Christians witnessed to Jesus' death and resurrection, not to his conception, birth and infancy. Martyrdom came to those who would not give up belief in the risen Jesus, not to those who insisted that Jesus spent time as an infant in Egypt. Yet the continuing drive to understand this non-king who was the King led to a deeper understanding of the origin of this King than even some specialness about his conception and birth. John writing the Fourth Gospel, almost certainly the last to be written, and (in my view) likely written in full knowledge of the first three gospels, says this King (John 18:28-19:22) existed before the beginning of time, the Word who was God became human flesh (1:1-14).
From the Johannine perspective everything about Matthew and Luke's birth narratives is credible: the Word became flesh makes angelic messages, miraculous conception, and comparisons between the baby Jesus and Herod or Caesar so to speak 'minor miracles' beside the 'great miracle' of the Incarnation.