That that is God's general plan of salvation. Are there exceptions? Perhaps.
The Bible also says: "And as it is appointed unto man once to die, and after this the judgment." This is also a general rule of God. Are there exceptions? Elijah, Enoch, And those that will be raptured.
I study my Bible not Augustine, so this is a moot point.
This is not a good illustration. Adam and Eve were created by God as God's children. Death means separation. You believe in eternal security don't you--OSAS. That is the way it was with Adam and Eve. Their sin separated them from God--cut off their fellowship. They didn't lose their salvation. In order to restore that fellowship God sacrificed an animal. Blood was shed to cover the sin. Fellowship was restored.
Did David believe he would meet his infant in paradise?
On what premise did he believe that?
All of the above had their chance to believe and refused to believe in their lifetime that Christ was God, the only way to heaven; that he died for their sins, paid the penalty. They rejected him.
Infants don't have that choice; are unable to believe.
We commit them to the mercy of God.
"Shall not the judge of all the earth do right?"