The comparing and contrasting of the two biblical women, Eve called ‘the mother of all living’ (Genesis 3:20) and the Virgin Mary who is the Mother of God, begins already in the 2nd Century in the writings of St. Justin the Martyr (d. 165AD) :
“‘We understand that he is born of the Virgin, in order that the disobedience caused by the serpent might be destroyed in the same manner in which it had originated. For Eve, an undefiled virgin, conceived the word of the serpent and brought forth disobedience. But the Virgin Mary was filled with faith and joy, when the Angel Gabriel announced to her the good tidings’ (Justin, Dialog., L, 45).
This passage is interesting inasmuch as it shows us that the parallelism between Eve and Mary is earlier than Irenaeus, and indeed goes back to the earliest Christian tradition.[…] St.Irenaeus stresses the parallelism between Eve and Mary in another passage:
‘The Virgin Mary is found obedient; when she said, ‘Behold the handmaid of the Lord, be it done unto me according to your word.’ But Eve is found disobedient; for she did not obey, being yet a virgin….as Eve proving disobedient became the cause of death both to herself and to all mankind: so also Mary having a husband fore-appointed, and nevertheless a virgin, being obedient, became to herself all mankind the cause of salvation. Therefore the Law calls her who was espoused to a man, though still a virgin, the wife of his who had espoused her, pointing to the unwinding which should come round from Mary to Eve; since in no other way can that which is knotted be undone, but by bending the loops of the knot in reverse order: that the first tie may be undone by the second and the second again disengage the first’ (III, 22; 959A-B).” (Jean Danielou, S.J., From Shadows to Reality, pp 43-43)