Before there was a "Bible," there was the Living Word and real human beings who spread the Good News. The early Church didn't survive merely because of writings.
[Bolding below is mine.]
"While the church was still a missionary institution in the midst of a heathen world, infant baptism was overshadowed by the baptism of adult proselytes; as, in the following periods, upon the union of church and state, the order was reversed. At that time, too, there could, of course, be no such thing, even on the part of Christian parents, as a compulsory baptism, which dates from Justinian’s reign, and which inevitably leads to the profanation of the sacrament. Constantine sat among the fathers at the great Council of Nicaea, and gave legal effect to its decrees, and yet put off his baptism to his deathbed. The cases of Gregory of Nazianzum, St. Chrysostom, and St. Augustine, who had mothers of exemplary piety, and yet were not baptized before early manhood, show sufficiently that considerable freedom prevailed in this respect even in the Nicene and post-Nicene ages. Gregory of Nazianzum gives the advice to put off the baptism of children, where there is no danger of death, to their third year.(452)
At the same time it seems an almost certain fact, though by many disputed, that, with the baptism of converts, the optional baptism of the children of Christian parents in established congregations, comes down from the apostolic age.(453) Pious parents would naturally feel a desire to consecrate their offspring from the very beginning to the service of the Redeemer, and find a precedent in the ordinance of circumcision. This desire would be strengthened in cases of sickness by the prevailing notion of the necessity of baptism for salvation. Among the fathers, Tertullian himself not excepted—for he combats only its expediency—there is not a single voice against the lawfulness and the apostolic origin of infant baptism. No time can be fixed at which it was first introduced. Tertullian suggests, that it was usually based on the invitation of Christ: 'Suffer the little children to come unto me, and forbid them not.'"
https://bible.org/question/what-are-historical-origins-infant-baptism
