Nope sadly, only Adam and eve where born born with complete innocence, which Got lost after sin entered there nature. What you propose is where all born with complete innocence, which re-writes every word in the bible.
Sadly your so far of the mark it's untrue, as you would rather defend this idea that it's unfair to say babies are not born with complete innocence, rather than defend idea that God wants to restore there innocence, which is what the Bible is all about.
Which is what the bible is all about, babies have innocence but only in sense they are not aware of there innocence being lost untill they hear the truth.
Even then they can't grasp it from an early age, and it carries long into there adulthood, like you, who then Go and tell there children the same thing, like the bible can't true, when it is.
All tho you feel your speaking the truth your actually telling them a lie.
BUT WAIT, you had innocence when you born alright but only because you never had any accountability, but as you start growing up there would of been many times the feeling of shame would of started to kick in for what ever reason you may have become embarrassed for.
Having complete innocence equals no shame, it's where Adam and eve walked in the Garden completely unaware they where naked, and before you say, they where just babies to, no they where not, Adam was given responsibility in the Garden before sinning which was a command that A baby could NOT follow.
So I have to tell you instead of getting all uptight about babies not having complete innocence, you should be focusing on what the lord has to do to restore there innocence and what he has to do, without there permission,
It starts with God appointing a guardian angel to babies, then as they grow up with lord in the wilderness, God speaks to them, and delivers his will to there conscience, which is called his enabling Grace, and one main attribute of that enabling grace is the prick to there conscience which gives them the will to choose the right thing.
You don't have to take my word for it either,.it's all recorded in scripture what I cite hear in hundreds of places