(The following was written in response to a question.)
I think that the best answer I can give you is this:
People were bringing little children to Jesus to have him touch them, but the disciples rebuked them. When Jesus saw this, he was indignant. He said to them, “Let the little children come to me, and do not hinder them, for the kingdom of God belongs to such as these. I tell you the truth, anyone who will not receive the kingdom of God like a little child will never enter it.” And he took the children in his arms, put his hands on them and blessed them. (Mark 10:13-16)
Our salvation is not based on knowledge about God (though knowledge about God can be helpful). Our salvation comes to us through faith, and I believe that faith is, at its core, being orientated towards the God who saves. The believers in the Old Testament did not have the knowledge about God that we have, but they were still saved because they trusted in the God who saves.
I believe that the faith of a child towards God is a saving faith and in some ways it is the best kind of faith to have. It almost seems easier for a child to believe than us adults. Children almost seem to have a natural ability to trust. Even as infants they know and trust their mothers. And I believe they can also know and trust their heavenly Father at a young age.
We have a picture in our home of Jesus with three children. When one of my daughters was only 18 months old, my wife was teaching her how to sing “Jesus Loves Me.” In the middle of the song, my daughter stopped and pointed at the picture. She made the connection between the song and the picture. I believe that was an indication of the faith that she already had.
So, yes, I think that children can have saving faith. It’s not logical, but we are talking about the things of God here and maybe saying that something is not logical is just another way of saying that it is beyond our comprehension.
May God bless you and continue to give his joy and peace,