Have you encountered the phrase “original sin” before? That’s essentially what you are talking about when you say a baby can sin. When you think about it, a baby can’t do much of anything on its own and certainly can’t choose to do something wrong. And yet, that baby has been born into a sinful world and is exposed to sin from the very beginning. I think of it as being like a baby that’s born into a very polluted world. Even though the baby has never smoked, from his first breath he is breathing pollution into his lungs and they’re not as pure as they should be.
Equally, his soul is not as pure as it should be because he’s being exposed to sin.
The Church says this in the Catechism:
403 Following St. Paul, the Church has always taught that the overwhelming misery which oppresses men and their inclination towards evil and death cannot be understood apart from their connection with Adam’s sin and the fact that he has transmitted to us a sin with which we are all born afflicted, a sin which is the “death of the soul”.291 Because of this certainty of faith, the Church baptizes for the remission of sins even tiny infants who have not committed personal sin.
From our first parents, sadly, we are exposed to sin and have an inclination to do wrong. Have you ever felt like St. Paul, who said, “For I do not do the good I want, but I do the evil I do not want” (Romans 7:19). And that’s because of sin.
The Church teaches that the sacrament of Baptism remits original sin. We’re cleansed and can start anew, we’re born again. What, then, happens to someone who dies without baptism? They’re still mired in original sin. The Church has addressed this issue and basically says we don’t know for sure what happens to these people, but we have hope in the mercy of God:
1261 As regards children who have died without Baptism, the Church can only entrust them to the mercy of God, as she does in her funeral rites for them. Indeed, the great mercy of God who desires that all men should be saved, and Jesus’ tenderness toward children which caused him to say: “Let the children come to me, do not hinder them,”64 allow us to hope that there is a way of salvation for children who have died without Baptism. All the more urgent is the Church’s call not to prevent little children coming to Christ through the gift of holy Baptism. (1257, 1250)