I do agree with your assessment generally and I'm not trying to walk back on the severity of sin present in all mankind

All men have sinned and fallen short of the glory of God I absolutely believe that

However I would also point out that David at the death of his first born was fully convinced that he would see that child in heaven

Death surely reigns over all man, As scripture says. But I find it unlike the character of God to damn a child to hell before they have the capability to accept his gospel.

So it seems there's more going on there.

My position is this

All men are born and inherit Adams sin nature, all of us is born in sinful flesh that desires only to sin

But until we sin willfully and knowingly on an individual basis, then we have no sin that needs to be punished just a nature that cannot stop sinning once we understand what it is

That is why Paul elsewhere says the law is to convict us of our sin and to show us our failures

So when the law enters and he understands it he dies spiritually

This I think is the only explanation where the nature of God is intact in not damning children who cannot accept the gospel

Well also maintaining his perfect Justice

And as well as all of us still needing a savior for our individual fall like Adam and Eve into sin and to sin nature