Mary's title being, the Mother of God, is a teaching and reflection on "Who Jesus Christ is", then on who Mary is.
The Early Church Fathers had no problem referring to Mary as the Mother of God. They saw it as a natural consequence of the Incarnation. It was not an affirmation that Mary was the originator of God the Father, but that she bore the God-Man, her Divine Son, Jesus, in her womb and as Revelation would show, would become incarnate for the sake of our salvation. As a consequence, Jesus is a Divine person, not a human person like many heretics were saying.
The Church's Scriptures that support Mary being the Mother of God [the God-bearer of Jesus]:
Even those in the community where Jesus lived recognized Mary as His mother
55 Is not this the carpenter's son? Is not his mother called Mary?
Mary's cousin Elizabeth also testifies that Mary is the Mother of [my Lord] God.
41 And when Elizabeth heard the greeting of Mary, the babe leaped in her womb; and Elizabeth was filled with the Holy Spirit 42 and she exclaimed with a loud cry, "Blessed are you among women, and blessed is the fruit of your womb! 43 And why is this granted me, that the mother of my Lord should come to me?
John acknowledges that Mary, the mother of Jesus, was at the marriage at Cana
1 On the third day there was a marriage at Cana in Galilee, and the mother of Jesus was there.
John acknowledges, for a second time, that Mary, the mother of Jesus, was at the foot of the Cross
25 So the soldiers did this. But standing by the cross of Jesus were his mother, and his mother's sister, Mary the wife of Clopas, and Mary Magdalene.