Well concerning how early this belief was seen let us look at the witnesses of this doctrine:
St. Irenaeus Against Heresies, bk III, ch 22, 4: 4. In accordance with this design, Mary the Virgin is found obedient, saying, Behold the handmaid of the Lord; be it unto me according to your word. But Eve was disobedient; for she did not obey when as yet she was a virgin. And even as she, having indeed a husband, Adam, but being nevertheless as yet a virgin (for in Paradise they were both naked, and were not ashamed, inasmuch as they, having been created a short time previously, had no understanding of the procreation of children: for it was necessary that they should first come to adult age, and then multiply from that time onward), having become disobedient, was made the cause of death, both to herself and to the entire human race; so also did Mary, having a man betrothed [to her], and being nevertheless a virgin, by yielding obedience, become the cause of salvation, both to herself and the whole human race. And on this account does the law term a woman betrothed to a man, the wife of him who had betrothed her, although she was as yet a virgin; thus indicating the back-reference from Mary to Eve, because what is joined together could not otherwise be put asunder than by inversion of the process by which these bonds of union had arisen; so that the former ties be cancelled by the latter, that the latter may set the former again at liberty. And it has, in fact, happened that the first compact looses from the second tie, but that the second tie takes the position of the first which has been cancelled. For this reason did the Lord declare that the first should in truth be last, and the last first. And the prophet, too, indicates the same, saying, instead of fathers, children have been born unto you. For the Lord, having been born the First-begotten of the dead, and receiving into His bosom the ancient fathers, has regenerated them into the life of God, He having been made Himself the beginning of those that live, as Adam became the beginning of those who die. Wherefore also Luke, commencing the genealogy with the Lord, carried it back to Adam, indicating that it was He who regenerated them into the Gospel of life, and not they Him. And thus also it was that the knot of Eve's disobedience was loosed by the obedience of Mary. For what the virgin Eve had bound fast through unbelief, this did the virgin Mary set free through faith.
Justin Martyr: Dialogue with Trypho, ch 100: and that He became man by the Virgin, in order that the disobedience which proceeded from the serpent might receive its destruction in the same manner in which it derived its origin. For Eve, who was a virgin and undefiled, having conceived the word of the serpent, brought forth disobedience and death. But the Virgin Mary received faith and joy, when the angel Gabriel announced the good tidings to her that the Spirit of the Lord would come upon her, and the power of the Highest would overshadow her: wherefore also the Holy Thing begotten of her is the Son of God; and she replied, 'Be it unto me according to your word.'
These here are two of the earliest apologetic writings of the Church, and already it was commonly viewed that Mary is the new Eve, as her Son is the new Adam. And we see here the comparison and contrast of the new and old Eve is similar to the comparison and contrast of the new and old Adam. It was Mary's obedience that unmade the disobedience of Eve. I think it would be a stretch to say that Mary as the new Eve was really disobedient like Eve and every other woman who has lived, but since she was obedient just once, she is now the new Eve. No I think that would be a huge stretch. Especially considering that Gabriel gave her the title of Full of Grace or Most Favored.
