The council of Ephesus confirmed that status in 4 century AD after Nestorius questioned it. Whoever "elevated" her, did so before the 4 Century. My bet is on Archangel Gabriel.
"My bet is on Archangel Gabriel."
You are right that the term Theotokos (which again, is specifically *not* the same term as "Mother of God" in Greek -- it is the Birthgiver of God, or Bringer-forth of God -- hence we Orthodox in the English speaking world leave the word untranslated) came long before the council in Ephesus.
Nestorius's avoidance of the term was odd enough within the Church that it drew attention to him, even though he had mostly kept his heretical beliefs to himself.
And while the Archangel may have used the term, we do know that something very close was used by St. Elizabeth, who called her "the mother of my Lord."