Babies Are Not Born in Sin

 We often turn to 1 John 3:4 for our definition of "sin" - a transgression of law.

But the New Testament uses the term more broadly than that one narrow definition. More generally, the term "sin" simply means "falling short of the target".

Paul uses this term in Romans 5-8 in this broader sense: Adam "fell short" of the target of obedience, and brought death into the world. This death then caused the entire cosmos to "fall short" of the target of its created ideal, which brings death to everyone, even those who are innocent of the type of "falling short" committed by Adam. There's a "falling short" that brings guilt, like Adam's, and there's a "falling short" that is not like Adam's, which still brings death even when there is no law to be broken.

So in the sense of "falling short" of law-keeping, it is correct to say that babies are not born in/with "sin".

But in the sense of "falling short" of what God intended in his creation, babies are born in "sin", and this is why innocent babies sometimes die. Such babies are not guilty of breaking law, and thus do not have sin in the way John uses the term, but they do have sin in the sense of falling short of the created ideal, as Paul uses the term.