Adam and Eve's sin in the Garden of Eve had consequences. Then sin entered the world and death through sin. We are born sinners and we are born mortals. When Adam and Eve were created it was possible for them not to sin and possible for them not to die. But for us it is different because of Adam and Eve.
Children are sinners by nature and environment.
It has been said that original sin is the only theological doctrine which can be proven. Every one who has had kids know that children sin. You tell them not to do something, and they will do it. They can be very mean and cruel on occasion. But the Bible says that until a certain age, which we call the age of accountability, children are not held eternally accountable for their sin.