And you are assuming they didn't.
Ummm no.The assumption was yours, your argument was based on it. I discussed the context the statement was given in and what it would have meant to the people he was speaking to.
You have several things working against you.
1. James 2:10 Says those who sin once are guilty of breaking the whole law
Don't see the relevance of that James was speaking of the Mosaic law which wasn't binding on Gentiles of Jewish children. Bar Mitzvah literally means 'son of the law'.
2. Secular science shows that infants lie before they talk
Do they know it's wrong?
3. Christ declaring He is the only way to the Father (children don't have this saving faith)
THe same Jesus who also said as you mention Matt 19:14
"Let the little children come to me and do not hinder them, for to such belongs the kingdom of heaven." But the question isn't whether Jesus leads little children to the father but whether these little innocents have committed any sins they are guilty of.
4. Bible speaking universally that all men are not righteous (Romans 3:15) and that "sin spread to all men" (Romans 5:12)
Again, Paul an adult speaking to adults, adults who didn't think little children were guilty of sin.
So, science and Scripture all indicate the position that all humans are in sin and those who have a soft spot for babies have no Scripture to back them up...as in none, zilch, nada. Yet the preponderance of Scripture (Psalms 51, Ephesians 1, Romans 3, Romans 5, etc. etc.) says the opposite and it takes mental gymnastics (and an misinterpretation of Matt 19:14) to say the opposite. Sorry, but such a position is intellectually wanting.
There are plenty of scriptures which say people die for their own sins not their father's, that talk about the age of accountability when children learn the difference between right and wrong, and you have Paul's own statement in Romans 7 where he talked about being alive before he understood the commandment then dying when he broke the commandment and sinned. Rom 7:7
What then shall we say? That the law is sin? By no means! Yet if it had not been for the law, I would not have known sin. For I would not have known what it is to covet if the law had not said, "You shall not covet." 8 But sin, seizing an opportunity through the commandment, produced in me all kinds of covetousness. For apart from the law, sin lies dead. 9 I was once alive apart from the law, but when the commandment came, sin came alive and I died.
Paul also fits Romans 5:12
and so death spread to all men because all sinned. But you have to look at how it worked itself out in Paul's life. Death spread to Paul because Paul sinned. but it didn't spread to him, couldn't spread to him, until he understood right and wrong, and did what he knew was wrong.
That's prophecy about Christ, so of course He refuses evil and chooses the good, unlike any other human.
Oh, we can know it too, and sometime even practice it, even Gentiles Rom 2:14. But Christ is the only one who never failed who always refused evil and always chose good. But interestingly, even Christ didn't know the difference between right and wrong when he was a baby. Isaiah 7:15
He shall eat curds and honey when he knows how to refuse the evil and choose the good.
16
For before the boy knows how to refuse the evil and choose the good.
You also see the age of accountability in Deut 1:39
And as for your little ones, who you said would become a prey, and your children, who today have no knowledge of good or evil, they shall go in there. And to them I will give it, and they shall possess it.
I believe that would be the correct interpretation of ROmans 5:17
"For if by the one mans offense death reigned through the one, much more those who receive abundance of grace and of the gift of righteousness will reign in life through the One, Jesus Christ."
Death comes through Adam. Whether we literally inherit his specific sin, or we inherit his sinfulness, it is through him we die, and we die because of sin.
Paul already explain how death reigned in Romans 5:12
and so death spread to all men because all sinned. Saying we inherited Adam's sin nature is a huge claim to make, it take much more than just using the idea to explain another verse. We need a clear statement of this concept, and it isn't found anywhere in scripture.
But of course, those who don't understand that God saves people, instead of people smart enough to have faith thereby saving themselves, they think that babies therefore are not liable for their sin, or they are somehow sinless.
However, the Scripture doesn't say this. The only way to the Father is through Christ. The only way to place faith in Christ is if God opens your eyes...so faith is an act of grace. So, if tons of adults die without saving grace, so do a ton of babies. It's pretty straight forward.
Irresistible grace is a different discussion

But I don't think tons of adults dying lost in their own sins means tons of innocent babies are lost too.
And, even by their standards they fall short, because no one always abides by the law that they are onto themselves.
"Now we know that whatever the law says, it says to those who are under the law, that every mouth may be stopped, and all the world may become guilty before God." (Romans 3:19)
Be careful not to read something that's not there. The quotation doesn't say "well, only those under the law are condemned." It says, unequivocally, "all the world may become guilty before God" as in those with no law and those with it.
The matter is settled and any other rendering rejects the Gospel and the necessity of having faith in Christ.
Paul is talking about Jews and Gentiles in that chapter. By the whole world Paul means both Jews and Gentiles are accountable to God. But he is still talking to adults about adults like themselves around the world. If Paul wanted to overturn the bible based Jewish teaching of age of accountability, he would have addressed it directly, he would have had to for his readers to understand he meant babies as well as grown ups. It makes sense to you when you already believe children are born stained with Original Sin to read Paul's 'all the world' as meaning babies as well as grown ups. But for Paul's readers who understood and assumed little children were innocent, they would never have read the passage that way. It would have seemed ludicrous. Writing to people like that, if Paul meant children too he would have had to explain it very clearly.