there is no exact explicit mention of mother mary as the "mediatrix" in the first few centuries. but the root of the teaching was definitely with the church fathers.
St. Irenaeus (130-202), in his famous Against Heresies (bet. 180-199) wrote:
“. . . so also Mary . . . being obedient, was made the cause of
salvation for herself and for the whole human race . . . Thus, the
knot of Eve’s disobedience was loosed by the obedience of Mary. What
the virgin Eve had bound in unbelief, the Virgin Mary loosed through
faith.”
(3, 22, 4; from W. A. Jurgens, The Faith of the Early Fathers, Collegeville, Minnesota: Liturgical Press, 1970, vol. 1, p. 93, #224)
“. . . for in no other way can that which is tied be untied unless the
very windings of the knot are gone through in reverse: so that the
first joints are loosed through the second, and the second in turn
free the first . . . Thus, then, the knot of the disobedience of Eve
was untied through the obedience of Mary.”
(Against Heresies, III, 22,4; from William G. Most, Mary in Our Life, Garden City, New York: Doubleday Image, 1954, 25)
St. Irenaeus wrote in Against Heresies, III, 21, 7:
On this account also, Daniel, foreseeing His advent, said that a
stone, cut out without hands, came into this world. For this is what
“without hands” means, that His coming into this world was not by the
operation of human hands, that is, of those men who are accustomed to
stone-cutting; that is, Joseph taking no part with regard to it, but
Mary alone co-operating with the pre-arranged plan. For this stone
from the earth derives existence from both the power and the wisdom of
God. Wherefore also Isaiah says: “Thus saith the Lord, Behold, I
deposit in the foundations of Zion a stone, precious, elect, the
chief, the corner-one, to be had in honour.” So, then, we understand
that His advent in human nature was not by the will of a man, but by
the will of God.
St. Ambrose of Milan (c. 339-397) wrote:
Mary was alone when the Holy Spirit came upon her and overshadowed
her. She was alone when she saved the world — operata est mundi
salutem – and when she conceived the redemption of all — concepit
redemptionem universorum.
(in Mark I. Miravelle, ditor, Mary: Coredemptrix, Mediatrix, Advocate: Theological Foundations, Santa Barbara, Califiornia: Queenship Publishing, 1995, p. 14; from Epist. 49,2; ML 16, 1154)
She engendered redemption for humanity, she was carrying, in her womb,
the remission of sins.
(in Miravelle, ibid., p. 14; from De Mysteriis III, 13; ML 16,393; De instit. Virginis 13,81; ML 16,325)
St. Ephraem of Syria (c. 306-373) called Mary the “dispensatrix of all goods.” (in William G. Most, Mary in Our Life, Garden City, New York: Doubleday Image, 1963, 48)
Basil of Seleucia (died c. 458) referred to her as the “Mediatrix of God and men.” (in Most, ibid., 48)
St. Cyril of Alexandria (d. 444) wrote:
“Hail, Mary, Mother of God, by whom all faithful souls are saved
[sozetai].
(in Miravelle, ibid., p. 13; from MG 77, 992, and 1033; from the Council of Ephesus in 431)
St. Andrew of Crete (c. 660-740) referred to Mary as the “Mediatrix of the law and grace” and also stated that “she is the mediation between the sublimity of God and the abjection of the flesh.”
(Nativ. Mariæ, Serm. 1 and Serm. 4, PG 97, 808, 865; in Miravelle, ibid., 283)
St. John of Damascus (c. 675-c. 749) spoke of Mary fulfilling the “office of Mediatrix.”
(Hom. S. Mariæ in Zonam, PG 98, 377; in Miravelle, ibid., 283)
The Protestant reference Oxford Dictionary of the Christian Church (ed. F. L. Cross, 2nd ed., Oxford Univ. Press, 1983, p. 561), states concerning Patriarch Germanus:
“Mary’s incomparable purity, foreshadowing the doctrine of the
Immaculate Conception, and her universal mediation in the distribution
of supernatural blessings, are his two frequently recurring themes.”
William Most comments:
“Mary, says St. Irenaeus, undoes the work of Eve. Now it was not just
in a remote way that Eve had been involved in original sin: she shared
in the very ruinous act itself. Similarly, it would seem, Mary ought
to share in the very act by which the knot is untied — that is, in
Calvary itself.”
(in Most, ibid., 25)
“Just as the human race was bound over to death through a virgin, so
was it saved through a virgin: the scale was balanced — a virgin’s
disobedience by a virgin’s obedience.”
(Against Heresies, V, 19, 1; cited in Most, ibid., 274)
And also the well-known Protestant patristics scholar J. N. D. Kelly says:
"The real contribution of these early centuries, however, was more positively theological, and consisted in representing Mary as the
antithesis of Eve and drawing out the implications of this. Justin was
the pioneer, although the way he introduced the theme suggests that he
was not innovating . . . Tertullian and Irenaeus were quick to develop
these ideas. The latter, in particular, argued [Against Heresies, 3,
22, 4; cf. 5, 19, 1] that Eve, while still a virgin, had proved
disobedient and so became the cause of death both for herself and for
all mankind, but Mary, also a virgin, obeyed and became the cause of
salvation both for herself and for all mankind. “Thus, as the human
race was bound fast to death through a virgin, so through a virgin it
was saved.” Irenaeus further hinted both at her universal motherhood
and at her cooperation in Christ’s saving work, describing [Ibid, 4,
33, 1] her womb as “that pure womb which regenerates men to God.”
(Early Christian Doctrines, San Francisco: HarperCollins, revised edition of 1978, 493-494, emphases added)
More citations are in https://www.patheos.com/blogs/davearmstrong/2017/03/mary-mediatrix-church-fathers-vs-james-white.html