The concept did not come out from no place.
Jesus said of little chilren, ". . . for of such is the kingdom of God. . . ."
The Greek word translated "little children" is παιδια plural of παιδιον.
Now a ruler named Jairus had a "little daugher" of a said age of twelve.
The Greek for little daughter being, θυγατριον.
The Greek ending
-ιον meaning little.
So the age of accountablility has been supposed to be to the age of twelve. This is a deduced interpertation from Scripture.
Since at birth a child was counted as 1 the age twelve should be our age of eleven.
There are those who teach the only saved little child is one from a family in which one parent is redeemed and therefore the children are safe until they make a decision.
All cultures distinguish between childhood and adulthood. Hebrew culture was no different. If I understand correctly, the “barmistpha” (spelling?) is the Jewish ceremony for adulthood and occurs at about age 13.
You are “deducing” from scripture something that was never taught, nor intended to be believed, I.e, there is a period of life when God holds all people blameless for their sins. They start out saved, but at some point (age of accountability) God begins to hold them accountable for sin, removing their names from His book of life.
What you believe is simply not supported in scripture.