There are some Christian confessions that erroneously claim infants should not be baptized. You might have even heard the claim that the apostles and early Church only baptized adults. Presented below is a small fraction of the evidence that supports the truth of our Catholic Faith with regard to the apostolic nature of infant baptism.

Born with a fallen human nature and tainted by original sin, children also have need of the new birth in Baptism to be freed from the power of darkness and brought into the realm of the freedom of the children of God, to which all men are called. The sheer gratuitousness of the grace of salvation is particularly manifest in infant Baptism. The Church and the parents would deny a child the priceless grace of becoming a child of God were they not to confer Baptism shortly after birth.
- Catechism of the Catholic Church, 2nd ed., (1997), n.1250
The practice of infant Baptism is an immemorial tradition of the Church. There is explicit testimony to this practice from the second century on, and it is quite possible that, from the beginning of the apostolic preaching, when whole "households" received baptism, infants may also have been baptized.
- Catechism of the Catholic Church, 2nd ed., (1997), n.1252

Lev. 12:3 - The circumcision of eight-day old babies was the way of entering into the Old Covenant.

Col. 2:11-12 - Baptism is the new "circumcision" for the New Covenant. Therefore, baptism is for babies as well as adults.

Mt. 18:2-5 - Jesus says unless we become like children we cannot enter into heaven. Therefore, why would they be excluded from baptism?

Acts. 16:15,33; Acts. 18:8; 1Cor. 1:16 – Whole households were baptized. Therefore, none who resided in the house were excluded. All, including infants were born-again in Christ.

Eph. 1:1, Eph. 6:1 - Paul addresses the "saints" of the Church, and among these were the children he exhorted to obedience. Children become saints of the Church only through baptism.

Tradition & Fathers
"And many, both men and women, who have been Christ's disciples from childhood, remain pure and at the age of sixty or seventy years..."
- St. Justin Martyr, First Apology (A.D. ~110-165)
"For He came to save all through means of Himself--all, I say, who through Him are born again to God--infants, and children, and boys, and youths, and old men."
- St. Irenaeus of Lyons, Against Heresies (A.D. 130-202)
"And they shall baptise the little children first. And if they can answer for themselves, let them answer. But if they cannot, let their parents answer or someone from their family."
- St. Hippolytus of Rome, Apostolic Tradition (A.D. 170-235)
"For this reason, moreover, the Church received from the apostles the tradition of baptizing infants too."