If we were medieval theologians, we could ask, “Did God choose someone else and get turned down before Mary?”
But realistically, it is hard to suggest, based on God’s knowing the future, that He asked someone who might say no.
Not that I’m suggesting Mary was the kind of girl who couldn’t say no...
It is biblical though. God regretted picking Saul in the OT.
Well he created Eve who said no. Part of his plan to introduce sin into the world?
It is a story of sin and redemption. Our response to God. God's call; Eve's response; Mary's response. Adam and the second Adam.
God created man (and woman) and he endowed them with free will.
Your position leads to absolving man of responsibility, Adam and Eve, Mary and you and I. Each of us is "picked" and has a choice of yes or no. Our choice matters and it is a real choice.