Just to add a little.
The Congregation for Doctrine of Faith issued an “Instruction on Infant Baptism” in 1980 which gives a history of our practice and explains the reasons for infant baptism in some detail. The
instruction can be found easily at the Vatican website among the pages of that congregation, and you will find it very useful.
Among the key points is that “Baptism is never administered without faith: in the case of infants, it is the faith of the Church. Furthermore, in accordance with the teaching of the Council of Trent on the sacraments, Baptism is not just a sign of faith but also a cause of faith.”
One of the chief pastoral points is that “Baptism, which is necessary for salvation, is the sign and the means of God’s prevenient love, which frees us from original sin and cmmunicates to us a share in divine life.” In using the term “prevenient,” the instruction is referring to divine election, by which we are first called by God rather than find God through our own initiative.
This is also treated in sections 1250-1252 of the Catechism of the Catholic Church. Infant baptism particular shows the free and unmerited gift of salvation that God offers to humanity.