Good question. I think it’s important to look at what baptism symbolizes and build from there. Under the old covenant baptism was performed on the 8th day of the infants birth.
Anyhow, circumcision was not optional but commanded by God and what were the benefits? The child then became a son of Abraham (Jewish) and was officially a part of the covenant family of God. Ask yourself, what would the consequences be of not having your child circumcised under old covenant law as commanded by God? So, if this was possible for infants under the Old Jewish Covenant, how much more is it possible for the New Covenant we have in Christ Jesus, Who says:
“Let the children be, do not keep them back from me; the Kingdom of Heaven belongs to such as these.” (Matthew 19:14)
Now the fundamental difference between baptism and circumcision is that baptism is a sacrament where as circumcision was a symbol, a symbol with real consequnces but it did not wash away sin:
“In Him, you were also circumcised with a circumcision not administered by hand, by stripping off the carnal body, with the circumcision of Christ. You were buried with Him in Baptism, in which you were also raised with Him through faith in the power of God, Who raised Him from the dead.” (Colossians 2:11-12)
So baptism is not merley washing away of sins but it is entering into the covenant of the Triune God where we recieve sonship with Jesus Christ and this mirrors circumcision under the old covenant. Now the scripture states that God is the same yesterday, today and forever, if he offered sonship to infants in the old testament and all of the covenant benefits how much more to those baptized into Christ?
The Catholic position has always been that we are all born into origanal sin and this differs from guilt. The child is not guilty of sin but is born with the stain of sin originating from the fall so the child lacks grace in the soul so the inclination toward sin is there and all people whether they have the ability to reason or not are affected by origanal sin.
The scriptures state that Christ came to save everyone and no one is excluded from needing salvation whether they are mentally ill or an infant, He is the savior of all men.
So in baptism the stain of origanal sin is washed away, we recieve the Holy Spirit and enter into the covenant family of God and become His adopted sons and daughters. There was no contention of this teaching for 1500 years until the 16th century and if anyone has prrof that there was please show me the evidence.
And so, while there is no specific mention of infants being Baptized, we do see numerous allusions to it in Scripture There is also no mention of the mentally handicapped being baptized but are we to assume they were not? For example, after Peter gives his public address on the day of Pentecost, Acts 2:37-39 tells us,
“Now when they heard this, they were cut to the heart, and they asked Peter and the other apostles, ‘What are we to do, my brothers?’ Peter said to them, 'Repent and be Baptized, every one of you, in the name of Jesus Christ for the forgiveness of your sins, and you will receive the gift of the Holy Spirit. For the promise is made to you and to YOUR CHILDREN and to all those far off, whomever the Lord our God will call.” (Acts 2:37-39)Also, Scripture gives us numerous accounts of entire households being Baptized. Here again, the Greek word for “household” assumes that children and babies are included:
Acts 16:14-15 – “One of them, a woman named Lydia, a dealer in purple cloth, from the city of Thyatira, a worshiper of God, listened, and the Lord opened her heart to pay attention to what Paul was saying. After she AND HER HOUSEHOLD had been baptized, she offered us an invitation …”
Acts 16:30-33 --“Then he (the jailer) brought them out and said, ‘Sirs, what must I do to be saved?’ And they (Paul & Silas) said, ‘Believe in the Lord Jesus and you AND YOUR HOUSEHOLD will be saved.’ So they spoke the Word of the Lord to him and to everyone in his house. He took them in at that hour of the night (midnight, v. 25) and bathed their wounds; then he and ALL HIS FAMILY were baptized at once.”
Acts 18:8 --“Crispus, the synagogue official, came to believe in the Lord along with his ENTIRE HOUSEHOLD, and many of the Corinthians who heard believed and were baptized.”
See also Acts 10:24-27 & 10:44-48 where Peter Baptizes the entire family of Cornelius.