All souls who have inhabited a body proceeding out of Adam's DNA must suffer physical death; that is, separation of the soul and spirit from a no-longer-functioning meat body system. That is the kind of death that the new-born infant must suffer sometime after birth. He is born to die. Even Jesus was. That is the kind of death brought in by Adam's sin.
But Adam's sin also caused spiritual death--the inability of man's spirit to communicate with God's Spirit. Unless that baby is rescued, he/she will the suffer Eternal death, the Lake of Fire.
When sin is not imputed, as with the babe who is not conscious of the law, the babe might have to experience an early physical death, but its original sin will be overlooked, and its soul and spirit will be given both Eternal and spiritual life: he will come under The Blood.
Neither the blood of bulls, nor of goats, nor of the water of human visible baptism can take away sins. Only Jesus' Blood can do that. And after being made aware of sin, of righteousness, and of imminent judging by God, the person who fails to appropriate Jesus' work and resurrection power will also die physically, remain spiritually dead, and be given over to Eternal but conscious death, ultimately in the lake of fire.
One who responds to this awareness by admitting his depravity and casting himself on God's unfailing mercy will experience the graceful spiritual covering and cleansing of Jesus' blood shed for him, and will have Jesus' righteousness imputed to him, and will pass immediately into spiritual life and communication with God and His Son through the Holy Spirit, will receive Eternal, abundant Life immediately, never to cease; and at an appropriate time chosen by The Father, will also have a new never-dying flesh body to house his/her preserved soul and spirit.
And in that Paradise, there will be individuals who, as babes, never committed sin and to whom the original sin transmitted with their temporary tent of Adam's flesh was never imputed to their account by God.
In this all, the proper use of water baptism, as a visible external announcement of an internal change by faith in Christ and His Blood, has no effect one way or the other. It only relates to the authorized enlistment of a person into His Church and into His service while on earth.
Water baptism can never take away sins. To think otherwise is both intellectually and spiritually foolish.
Two thoughts:
1) It's an assumption on your part that "original sin" will be overlooked. In fact, if "all have fallen short" of the glory of God, and if "no one can see the Kingdom of heaven" unless they are born again, then it is absolute that God overlooks no sin, even original, for all sin is heinous in the sight of God.
2) The scripture makes not just physical death, but spiritual "condemnation" universal by imputation of Adam, in parallel to the justification that is imputed by Christ to believers:
Rom 5:16 And not as it was by one that sinned, so is the gift: for the judgment was by one to condemnation, but the free gift is of many offences unto justification.
If eternal life is a matter of justification, then "judgment and condemnation" must not refer merely to physical death, but to an entire condemnation entirely.
Furthermore, going back to the point that Paul made: where there is no law, there is no sin; nevertheless, from Adam to Moses death reigned. Clearly these men who were not under any law were subject to death and sin, and this can only be through the condemnation of Adam that passed onto all men, not their "many offenses," but "one offense" passing on death and judgment and condemnation to all.