Yes, or He could’ve prevented Adam or any descendants from committing the original sin to begin with. But God prizes man’s freedom; He “ left man in the hand of his own counsel” for His purposes, determining to produce something with that freedom, something greater than He began with.
Adam played his role in our falling while Mary played a part in our rising. God graces certain people at certain times to advance His kingdom in certain ways and Mary was so graced, for the benefit of us all. While He’s still unwilling to totally override your will, we’re completely lost unless He works in this world to bring us into the light. And He often chooses to use people for that purpose. Even in our lives right now He can bring people and circumstances to bear to help us in making the turn towards faith, or for whatever reason. Mary simply had a very large and favored role to play in that same capacity.