Your claim is pure nestorianism. A woman gives birth to a person, not to a nature. In case of Mary, she gave biorth to the entire second person of the Trinity, and by extension, she is mother of God. No, it does not mean that God has his beginning with Mary. Please read the Ephesian canons, a reference to which I posted in 67.
"Calling Mary either Theotokos or "Mother of God" (ÌÑ ÈÕ) was never meant to suggest that Mary was coeternal with God, or that she existed before Jesus Christ or God existed. The Church acknowledges the mystery in the words of this ancient hymn: 'He whom the entire universe could not contain was contained within your womb, O Theotokos.'"