The Hail Mary, also commonly called the Ave Maria (Latin) or Angelic Salutation, traditionally opens with "Holy Mary, Mother of God, pray for us sinners, now and at the hour of death."
When the Pharisees quibbled about Jesus' age in John 8:57, Jesus shocked them saying he was before Abraham. This makes the Hail Mary prayer impossible. Being God, Jesus did not begin his existence with a mother. She did become mother to a fleshly body which became the temple of God's Spirit, but she was never considered the Mother of God. Of course she was highly favored but never reverenced as God's mother.
Age sequences have regard to Jesus body. Mary is called the mother of Jesus several times, but only to identify her, not to deify her as the Mother of God. Jesus never refers to her as His mother in the text, but did refer to her as "Woman" (Jn. 2:5). Once when someone referred to her as His mother, He corrected them saying those hearing His word were His family (Mt. 12:49). The Old Testament is replete with passages relating Jesus' existence prior to visiting the earth in a fleshly body. Scholars have written much on various Old Testament accounts of Jesus. Paul affirmed it was Jesus who performed miracles for the Israelites in the wilderness of wanderings (I Cr. 10:4).
Lord, as in "Lord Jesus," is from the Greek word Kurios. It corresponds to the Hebrew word YHWH or Jehovah in the Old Testament, also translated LORD. This seems to indicate Jesus was the Angel of the Lord during the Old Testament days. It was He who sought out Hagar when she had fled into the wilderness from Sarah (Gen. 16:13). When He appeared to her, she addressed Him as, "You are the God who sees" (NKJV).
Consider also the appearance of the Lord to Abraham in Genesis 18 to inform him of Isaac's, miraculous birth and the destruction of Sodom and Gomorrah. This indicates Jesus performed miracles long before the wilderness episode. In the inspired apostle John's gospel (1:1-3), He is named as the creator of all things at the very beginning.
He forbad Abraham from offering his son as a sacrifice (Gen. 22). It was He who wrestled with Jacob in his dream and blessed him (Gen. 32); It was He who confronted Balaam by speaking from his Donkey (Num. 22); it was He who commissioned Moses at the burning bush authorizing his mission to Egypt to confront Pharaoh. It was on that occasion that He identified Himself as the I AM, a term Jesus applied to Himself (John 8:58; 18:5, 6). From Genesis to Revelation, all the mountains and dusty trails in between are alive with Jesus' presence. From Pharaoh to Nero, to Hitler and all other diabolical tyrants, none have been able to erase His presence. Confining Jesus to the New Testament would be like attempting to confine the sun to a single spot in the sky.
Check the references regarding "Angel of the Lord" and "I AM" in a good concordance or Bible search program and you will be amazed at what you find. Assigning Mary the title Mother of God is a vain attempt to deify her with a position nowhere revealed in the New Testament.
She was without doubt the most blessed of all women to birth the body that housed Jesus, but well-meaning as it may be by those who call her so, she was not the Mother of God. I think she would have been horrified at this title.