"In these, baptism by water is only the event at the end of a confession of faith which had to be learnt by heart"
No not at all unless you cherry pick history, for example.
"He [Jesus] came to save all through himself; all, I say, who through him are reborn in God: infants, and children, and youths, and old men. Therefore he passed through every age, becoming an infant for infants, sanctifying infants; a child for children, sanctifying those who are of that age . . . [so that] he might be the perfect teacher in all things, perfect not only in respect to the setting forth of truth, perfect also in respect to relative age" (Against Heresies 2:22:4 [A.D. 189]).
"‘And [Naaman] dipped himself . . . seven times in the Jordan’ [2 Kgs. 5:14]. It was not for nothing that Naaman of old, when suffering from leprosy, was purified upon his being baptized, but [this served] as an indication to us. For as we are lepers in sin, we are made clean, by means of the sacred water and the invocation of the Lord, from our old transgressions, being spiritually regenerated as newborn babes, even as the Lord has declared: ‘Except a man be born again through water and the Spirit, he shall not enter into the kingdom of heaven’ [John 3:5]" (Fragment34 [A.D. 190]).
"Baptize first the children, and if they can speak for themselves let them do so. Otherwise, let their parents or other relatives speak for them" (The Apostolic Tradition 21:16 [A.D. 215]).
"Every soul that is born into flesh is soiled by the filth of wickedness and sin. . . . In the Church, baptism is given for the remission of sins, and, according to the usage of the Church, baptism is given even to infants. If there were nothing in infants which required the remission of sins and nothing in them pertinent to forgiveness, the grace of baptism would seem superfluous" (Homilies on Leviticus 8:3 [A.D. 248]).
"The Church received from the apostles the tradition of giving baptism even to infants. The apostles, to whom were committed the secrets of the divine sacraments, knew there are in everyone innate strains of [original] sin, which must be washed away through water and the Spirit" (Commentaries on Romans 5:9 [A.D. 248]).
Cyprian of Carthage
"As to what pertains to the case of infants: You [Fidus] said that they ought not to be baptized within the second or third day after their birth, that the old law of circumcision must be taken into consideration, and that you did not think that one should be baptized and sanctified within the eighth day after his birth. In our council it seemed to us far otherwise. No one agreed to the course which you thought should be taken. Rather, we all judge that the mercy and grace of God ought to be denied to no man born" (Letters 64:2 [A.D. 253]).
"If, in the case of the worst sinners and those who formerly sinned much against God, when afterwards they believe, the remission of their sins is granted and no one is held back from baptism and grace, how much more, then, should an infant not be held back, who, having but recently been born, has done no sin, except that, born of the flesh according to Adam, he has contracted the contagion of that old death from his first being born. For this very reason does he [an infant] approach more easily to receive the remission of sins: because the sins forgiven him are not his own but those of another" (ibid., 64:5).