God existed before Mary did, so how can she be his mother?
To give birth to a god, one might reasonably expect the mother to be a god. Is Mary a god?
Nobody ever said that Mary gave birth to the eternal, triune God. The title “Mother of God” NEVER NEVER NEVER signified that Mary preceded, or gave rise to, or caused, or gave birth to, the eternal triune God.
Mary conceived and gave birth to the incarnate Son of God, the Second Person of the Trinity.
Since the incarnate Son of God, Jesus Christ, is God, and Mary conceived and gave birth to him, and because he is ONE PERSON, Mary is the mother of God.