“Let the children come to me, do not hinder them; for to such belongs the kingdom of heaven.”
The Church teaches that someone who is invincibly ignorant of God’s revelation concerning the necessity of baptism can be saved without the sacrament. But this applies only to someone who has the use of intellect and will to seek truth and do the will of God in accord with their understanding of it. So, the question is, “What happens to infants to who die without baptism? They don’t have the use of their intellect and will.”
Some theologians have proposed the idea of Limbo for the children, which is a state of the afterlife akin to that of the Old Testament righteous saints before they went to heaven—a state of natural bliss that is not heaven, hell, or purgatory (see Luke 16:19-31).
Traditionally, the Magisterium explicitly defended the doctrine of Limbo as a legitimate theological opinion. In his 1794 papal bull Auctorem Fidei, Pope Pius VI called the rejection of Limbo by the Jansenists “false, rash, and injurious to Catholic schools.”
Although the Magisterium has never rejected Limbo as an acceptable and legitimate teaching, it has more recently proposed another way to approach the topic of unbaptized infants. For example, the Catechism of the Catholic Church teaches that “the Church can only entrust them to the mercy of God,” and then gives two reasons as to why we can “hope that there is a way of salvation” for these children: 1) God desires all men to be saved, and 2) Jesus was tender toward children (CCC 1261).
The bottom line is that the Church doesn’t know with certainty whether children who die without baptism receive the Beatific Vision or exist in Limbo. The simple reason for such agnosticism is that it’s not revealed to us. This testifies to the humility of the Church and her concern for preaching only what Christ has revealed. In the end, however, we do have reason to hope for the salvation of unbaptized infants. And that’s something that we can take comfort in.