I work with children in a day care that is part of the Church of God. Naturally, all of the employees except me are of the Church of God, which is fine by me. I am non-denom. I find it curious that one of my co-workers stated that the children in my toddlers and twos class are "sin-free." I feel a bit odd asking anyone there about it since they are all COG. I don't understand how a human born of Adam and fallen short of the glory of God could be free from sin. I understand there is an age of accountability around 12 or 13, but does the COG teach that young children are "sin-free"?
The Church of God by Faith (not sure if there is a distinction like there is between Churches of Christ) does officially hold to original sin. However, many individual members of all denominations have *'s on that doctrine, if not outright reject it. One of the *'s being an age of accountability that you mentioned, before which salvation is given without formal repentance, baptism, and so on depending on denomination. For example, many hold that an aborted baby would go to heaven irrespective of the guilt they believe comes by way of original sin.
(As an addition, the doctrine of original sin doesn't come from passages about or addressing the theology of the actual original sin of Adam and Eve. Rather it comes from passages that are poetic in form and are in the context of repenting in extremely serious circumstances. I.E. Psalm 51, where David has been convicted of adultery and murder and is about to face strong consequences. As such, the doctrine of guilt at birth is justifiably debated among believers).