We are not told anywhere in scripture what the age of responsibility is. That is not surprising as it will vary depending on the personality, experiences and environment of the child.
In addition, “responsibility” can mean several things. A child learns what sin is as soon as they understand the word “no”. They grow in responsibility as they learn more about what God requires. Eventually a child is old enough to make a decision about whether they will be baptised and dedicate their life to God. For some children that might come in their early teenage years, for others it may not come until much later.
For people who grow up without hearing about the gospel at all, they may never be responsible to God. That is why not all will be raised to judgement. In Daniel 12 we read
And many of those who sleep in the dust of the earth shall awake, some to everlasting life, and some to shame and everlasting contempt. (Daniel 12:2)
The implication of “many” awaking at the resurrection is that some will not be raised. Presumably they are people who have never been responsible for their sins. As Paul wrote “sin is not counted where there is no law” (Rom 5:13).