If a child picks up a loaded gun and shoots his brother and kills him, he has broken the law. He committed murder. However, because he is a child and had no understanding of the consequences of his actions, the law will find him not guilty. Even in our wicked world, there is mercy to be found.
The same is true of children who sin in context of God's laws. Yes, he breaks God's laws, but it is in ignorance. Christ has atoned for that sin.
Children will and do sin because it is in their nature to do so, but just as God made provision for sins of ignorance in the OT, so Christ has made provision for those sins through His blood under the New Covenant.