When the Redeemer declares (John 3) that it is necessary to be born again of water and the Holy Ghost in order to enter the Kingdom of God, His words may be justly understood to mean that He includes all who are capable of having a right to this kingdom. Now, He has asserted such a right even for those who are not adults, when He says (Matthew 19:14): "Suffer the little children, and forbid them not to come to me: for the kingdom of heaven is for such." It has been objected that this latter text does not refer to infants, inasmuch as Christ says "to come to me". In the parallel passage in St. Luke (18:15), however, the text reads: "And they brought unto him also infants, that he might touch them"; and then follow the words cited from St. Matthew. In the Greek text, the words brephe and prosepheron refer to infants in arms.
Moreover, St. Paul (Colossians 2) says that baptism in the New Law has taken the place of circumcision in the Old. It was especially to infants that the rite of circumcision was applied by Divine precept. If it be said that there is no example of the baptism of infants to be found in the Bible, we may answer that infants are included in such phrases as: "She was baptized and her household" (Acts 16:15); "Himself was baptized, and all his house immediately" (Acts 16:33); "I baptized the household of Stephanus" (1 Corinthians 1:16).
To the objection that baptism requires faith, theologians reply that adults must have faith, but infants receive habitual faith, which is infused into them in the sacrament of regeneration. As to actual faith, they believe on the faith of another; as St. Augustine (De Verb. Apost., xiv, xviii) beautifully says: "He believes by another, who has sinned by another."
And, the proof that the Early Church DID baptise infants ,is from here by St. Cyprian of CarthageIn respect to the case of infants, which you say ought not to be baptised within the second or third day after birth, and that hte law of ncient circumcision be regarded, so that you think that one who is just born should not be baptised and sanctified within the eighth day,we all thought very differently in our council. For in this course which you thought was to be taken, no one agreed; but we all rather judge that the mercy and grace of God is not to be refused to any one born of man.. we ought to shrink from hindering an infant, who being lately born, has not sinned, except in that, being born after the flesh accrding to Adam, he has ontracted teh contagion of the ancient death as its earliest birth, who approaches the more easily on this very account to the reception of the forgiveness of sins -- that to him are remitted, not his own sincs, but the sins of another (Adam)and from Origen (185-254 AD)The Church received from the Apostles the tradition of giving Baptism even to infants. For the Apostles, to whom were committed teh secrets of divine mysteries, knew that there is in everyone the innate stains of sin, which must be washed away through water and the Spiritand from St. AugustineWho is so impious as to wish to exclude infants from the kindgom of heaven by forbidding them to be baptised and born again in Christ? This the Church always had, always held; this she received from the faith of our ancestors; this she perserveringly guards even to the end
Whoever says that even infants are vivified in Christ when they depart this life without the participation of His Sacrament (Baptism), both opposes the Apostolic preaching and condemns the whole Church which hastens to baptize infants, because it unhesitatingly believes that otherwise they can not possibly be vivified in Christ,"
This is an improper use of the term sola scriptura. As one of them 'types' myself, that isn't the issue here.