There are a few voices that may point to this, but of course there is also a danger of creating a doctrine based off of one verse.
In 2 Samuel 12:21-23 we can see an instance where this is present. This verse could be interpreted more than one way. One way would be to say David would see this child after he dies, or it could only mean that David will die eventually as the child did, but he does not have power to bring the child back to life.
21 Then his servants said to him, “What is this thing that you have done? You fasted and wept for the child while he was alive; but when the child died, you arose and ate food.” 22 He said, “While the child was still alive, I fasted and wept, for I said, Who knows whether the Lord will be gracious to me, that the child may live?’ 23 But now he is dead. Why should I fast? Can I bring him back again? I shall go to him, but he will not return to me.”
We do know that there is a tradition for an age of accountability within Judaism. This was held according to Genesis 2:18, where tradition is held that it was at age 13 Isaac was weaned, and given responsibilities as an adult.
Within the tradition, boys are considered responsible for their actions at age 13, and girls at 12 (I believe this is due to the idea that girls mature faster, and most girls reach puberty before boys). Until they reach the age of which they become responsible for their actions and observance of the law, their parents held responsibility for actions and observances instead.***
In Romans 7 Paul speaks of how there was a time when he did not understand the Law, therefore did not realize that the sins he committed were wrong. Once he realized that they were wrong, that is when sin came to power over him.
When speaking of children, we must also realize that we don't necessarily know the full extent of what children may know. I remember being a young child and believing in God. Although I knew nothing of Jesus, I knew there was God, and at the time that's all that I needed to know. I did not understand until I was 11 years old what salvation even was, and even after still did not fully understand it. It's very plausible that even small children have realization that there is God, even without knowing Jesus.
This may be part of why Jesus warned against misguiding children. They come to faith easily, but false teaching can tear them away from their belief in God. Parents, and other adults children come into contact with should be responsible for teaching them about God and Christ.
Paul also says that even for those who don't know Jesus, that creation showed the invisible qualities of God (Romans 1:20)
One argument against the age of accountability is that we are guilty of sin at birth.
One verse already used here for that is Psalm 58:3, but to look at the context of the chapter, it is not speaking of all people being evil. It is speaking of those who are wicked (against God),