Mosiah 3

 King Benjamin taught - 

"...even if it were possible that little children could sin they could not be saved; but I say unto you they are blessed; for behold, as in Adam, or by nature, they fall, even so the blood of Christ atoneth for their sins.

17 And moreover, I say unto you, that there shall be no other name given nor any other way nor means whereby salvation can come unto the children of men, only in and through the name of Christ, the Lord Omnipotent.

18 For behold he judgeth, and his judgment is just; and the infant perisheth not that dieth in his infancy; but men drink damnation to their own souls except they humble themselves and become as little children, and believe that salvation was, and is, and is to come, in and through the atoning blood of Christ, the Lord Omnipotent.

19 For the natural man is an enemy to God, and has been from the fall of Adam, and will be, forever and ever, unless he yields to the enticings of the Holy Spirit, and putteth off the natural man and becometh a saint through the atonement of Christ the Lord, and becometh as a child, submissive, meek, humble, patient, full of love, willing to submit to all things which the Lord seeth fit to inflict upon him, even as a child doth submit to his father."  (Mosiah 3:16–19)

I think the just of this is the children are not born in sin or sinful.  They are not the natural man at birth, but become so.  Thus the natural needs to become a saint though the atonement.  He cannot do it on his own.