Would you say that Mary was predestined to be the mother of Christ ?
If we look at the necessary requirements for the Savior to fulfill the OT prophecy, He had to have a specific lineage which He had through Mary and her husband Joseph.. His father by adoption ...The bible says that when the time was right (Gal4:4) He sent His son ..So the timing of Christ's arrival was to coincide with a system of roads and transportation that would allow for the gospel to spread..
So the mother and fathers existence had to coincide with the right political environment
Was all this happenstance?
I hate to use the term predestined cause there is a lot of baggage attached to it. I will state that from all time God has always known that man would fall and that He would promise them salvation. That being true He also knew how He would save us.
But what God always knew is not what we know at any set time. Adam did not know he would sin before he disobeyd God and yielded to temptation. Mary did not know she would say yes until the angel appeared.
So neither of them had the knowledge they were acting according to God’s sovereign plan. One disobeyed and one obeyed. Both were acting under their own will and own ability to make a free choice. Yet God’s hand was upon both. Is that contradictory? I don’t think so because as I stated before God is outside of time.
I do agree that yes the time of the Incarnation was the right time and for the reasons you state. Roman roads and Roman peace.
Could God have chosen another way of Salvation? Yes, but He did not. Remember the angels who rebelled did so because they could not abide the idea of God humbling Himself to become one of us.