However, advent is celebrated as if Christ’s Incarnation occurred at His birth. Any thoughts?
When I was growing up, the Annunciation was a holy day of obligation in the United States. Not anymore, and I miss that! I can still attend mass that day, of course, but it’s not the same as attending mass with a much larger group and with music, etc. My son’s school always has the kids go to morning mass that day, even if it’s not one of their regular mass days. But I digress…
The incarnation did indeed take place at the Annunciation. Christmas is a celebration of the birth of Christ – as the chant says, “the nativity (i.e., birth) of our Lord Jesus Christ according to the flesh.”
Liturgically there is more emphasis on the Nativity rather than the incarnation. Why? Well, it would have been a little weird to have shepherds and wise men worshiping the child in Mary’s belly.St John the Baptist has that moment of recognition while in Elizabeth’s womb, but let’s consider him an exception, being himself an unborn infant at the time
At that time in history, people hoped for a successful outcome to pregnancy; but it would have been understood that the life of the mother and the child would always be in jeopardy, during the pregnancy and especially at birth and shortly after delivery. And the science of human development in the womb made this time somewhat mysterious, regarding when life began, when the soul and body were united, and so on.
It is no wonder, then, that the Nativity, the
visible presence of Christ in the world, would take liturgical precedence over the Incarnation.
Perhaps there is also more for us to consider and apply to our own spiritual lives in the gospel’s birth narratives than in the Incarnation narrative. While I strive to imitate Mary’s fiat, and her Magnificat, I find much more spiritual food, as it were, in considering (for example) making room for Christ in my life; worshiping Him as He reveals Himself rather than how I expect or desire; leaving all behind to seek and find Him; following in obedience and immediacy when God commands (as He did in a dream to Joseph); and so on…
Well, I’m no theologian, and there’s probably just some really simple one sentence answer to your questions

But this has been a lot of fun for me to consider, so I appreciate you starting this thread.
God bless you!
Gertie