Jesus is referred to repeatedly in old testament also. His name is Yeshua which means salvation. Read a Hebrew bible or a Hebrew names bible, Yeshua is named many many times. Yeshua always was and Mary did not always exist therefore she did not and could not have given birth to God.
Jesus Christ is the Second Person of the Trinity, who was God from all eternity, and who became man in time. Mary gave birth to him, in time.
Since he is one person, Mary is called “Mother of God.”
The title was never intended to imply that Mary gave birth to the Second Person of the Trinity in eternity.
But since he is one Person, not two persons, and because she is his mother, she is called “Mother of God.”
The objection that Mary is a creature, who did not exist from eternity, is an objection to something that nobody ever said or believed.