Which Apostle does he mention taught the doctrine verbally? Does he actually quote an immediate “successor?”
I’m pretty certain like Jesus some things that the Apostles did were not written. These are what we Catholic called Tradition with a capital “T.” It was orally handed down from the Apostles to their successors.
To answer your questions, I would say all of the Apostles taught it.
The earliest record we have about Mary being virgin was written around 2nd Century.
“And indeed it was a virgin, about to marry once for all after her delivery, who gave birth to Christ, in order that each title of sanctity might be fulfilled in Christ’s parentage, by means of a mother who was both virgin, and wife of one husband. Again, when He is presented as an infant in the temple, who is it who receives Him into his hands? Who is the first to recognize Him in spirit? A man just and circumspect,’ and of course no digamist, (which is plain) even (from this consideration), lest (otherwise) Christ should presently be more worthily preached by a woman, an aged widow, and the wife of one man;’ who, living devoted to the temple, was (already) giving in her own person a sufficient token what sort of persons ought to be the adherents to the spiritual temple,–that is, the Church. Such eye-witnesses the Lord in infancy found; no different ones had He in adult age." Tertullian, On Monogamy, 8 (A.D. 213).
Another record is the Protoevangelium of James 4, 7 [A.D. 120)
And behold, an angel of the Lord stood by [St. Anne], saying, ‘Anne! Anne! The Lord has heard your prayer, and you shall conceive and shall bring forth, and your seed shall be spoken of in all the world.’ And Anne said, ‘As the Lord my God lives, if I beget either male or female, I will bring it as a gift to the Lord my God, and it shall minister to him in the holy things all the days of its life.’ . . . And [from the time she was three] Mary was in the temple of the Lord as if she were a dove that dwelt there" (Protoevangelium of James 4, 7 [A.D. 120]).
“And when she was twelve years old there was held a council of priests, saying, ‘Behold, Mary has reached the age of twelve years in the temple of the Lord. What then shall we do with her, lest perchance she defile the sanctuary of the Lord?’ And they said to the high priest, ‘You stand by the altar of the Lord; go in and pray concerning her, and whatever the Lord shall manifest to you, that also will we do.’ . . . [A]nd he prayed concerning her, and behold, an angel of the Lord stood by him saying, ‘Zechariah! Zechariah! Go out and assemble the widowers of the people and let them bring each his rod, and to whomsoever the Lord shall show a sign, his wife shall she be. . . . And Joseph [was chosen]. . . . And the priest said to Joseph, ‘You have been chosen by lot to take into your keeping the Virgin of the Lord.’ But Joseph refused, saying, ‘I have children, and I am an old man, and she is a young girl’” (ibid., 8–9).
“And Annas the scribe came to him [Joseph] . . . and saw that Mary was with child. And he ran away to the priest and said to him, ‘Joseph, whom you did vouch for, has committed a grievous crime.’ And the priest said, ‘How so?’ And he said, ‘He has defiled the virgin whom he received out of the temple of the Lord and has married her by stealth’” (ibid., 15).
“And the priest said, ‘Mary, why have you done this? And why have you brought your soul low and forgotten the Lord your God?’ . . . And she wept bitterly saying, ‘As the Lord my God lives, I am pure before him, and know not man’”