A baby is not born with sin, original or otherwise. A baby is born with mortality. This means it can die. It is not a matter of innocence or lack of it. It does not have to sin in order to die.
Mortality is a result of Adam’s sin; being his progeny we inherit his nature. We are born with a propensity to sin due to Adam eating the fruit of the tree of the knowledge of good and evil. We do not actually commit sin until we reach an age when we can differentiate right from wrong.When we reach this age we all sin because we have insufficient self-control.
Only those old enough to understand and obey the gospel can be saved from death.
We are all as clay in the hands of the potter. God gives life and he is able to take it away on his terms, not ours. We are not in a position to impose our opinions upon God.
I hope you find this helpful.