That depends on whose Original Sin you are talking about. According to this Wikipedia article on Original Sin, it has a wide variety of meanings and definitions depending on which church you go to and what Christian tradition you adhere to. LDS believe in a limited version of the Original Sin, but not the full-blown version of it that some Christian churches believe in. We accept that aspect of Original Sin that says that as a consequence of the sin of Adam, mankind has acquired a tendency or disposition to commit sin. This is clearly taught in the Book of Mormon:
Mosiah 3:19 “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.”
Ether 3:2 “. . . for we know that thou art holy and dwellest in the heavens, and that we are unworthy before thee; because of the fall our natures have become evil continually; nevertheless, O Lord, thou hast given us a commandment that we must call upon thee, that from thee we may receive according to our desires.”
But we reject that aspect of it that says that mankind is guilty because of the Original Sin. That has been the traditional Christian theology of the Original Sin. According to that theology, a man is guilty because of the Original Sin, even if he himself has not done anything wrong. That has been the logic behind infant baptism. According to that theology, a newborn infant is guilty not because he did something wrong, but because Adam did something wrong; and he will go to hell if he died in infancy without baptism. That is the aspect of the Original Sin that we reject completely. Our second Article of Faith states: “We believe that men will be punished for their own sins, and not for Adam’s transgression.” That is why we don’t baptize infants. We believe that all infants who die in infancy will go to heaven without the need for baptism.
As regards infant baptism, it was not a practice of the early church; it was a later development. Jesus and His Apostles did not baptized little children. Catholics would say otherwise; but they have no evidence to prove it. Not only is there no direct evidence that it was practiced; there is even evidence against it. It contradicts the theology of the gospel taught in the New Testament. One obvious reason is that repentance was a necessary prerequisite to baptism; and since infants cannot repent, they cannot fulfill the necessary requirement for baptism. Another obvious reason is that baptism was performed for the remission of sins. Again, since infants cannot sin, their baptism cannot have any theological validity—unless, of course, you believed that infants have “sinned in Adam;” which was indeed the original catholic position regarding infants—hence their doctrine of infant baptism. Here are the scriptural references:
Matthew 3:6 “And were baptized of him in Jordan, confessing their sins.”
Matthew 3:11 “I indeed baptize you with water unto repentance: but he that cometh after me is mightier than I, whose shoes I am not worthy to bear: he shall baptize you with the Holy Ghost, and with fire.”
Mark 1:4 “John did baptize in the wilderness, and preach the baptism of repentance for the remission of sins.”
Luke 3:3 “And he came into all the country about Jordan, preaching the baptism of repentance for the remission of sins.”
Acts 2:38 “Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.”
Acts 19:4 “Then said Paul, John verily baptized with the baptism of repentance, saying unto the people, that they should believe on him which should come after him, that is, on Christ Jesus.”
Acts 22:16 “And now why tarriest thou? arise, and be baptized, and wash away thy sins, calling on the name of the Lord.”
These requirements obviously cannot apply to infants, who can neither repent, nor have they committed any sins that need to be “remitted”.
Another obvious indication is that Jesus clearly taught that little Children are unconditionally saved, without the need for any sacraments:
Matthew 19:14 “But Jesus said, Suffer little children, and forbid them not, to come unto me: for of such is the kingdom of heaven.”
Mark 10:14 “But when Jesus saw it, he was much displeased, and said unto them, Suffer the little children to come unto me, and forbid them not: for of such is the kingdom of God.”
Luke 18:16 “But Jesus called them unto him, and said, Suffer little children to come unto me, and forbid them not: for of such is the kingdom of God.”
So not only there is no evidence for infant baptisms in the primitive church; all the available evidence points in the contrary. Therefore we can safely conclude that infant baptism was not a practice of the early Christian church.
When I have discussed this subject with Catholics, they nearly always respond by saying that the Catholic Church does not teach that an infant will go to hell without baptism! That may be true today; but it was not always so. That is a relatively new development. The earliest Catholic teaching was that infants will go hell without baptism. Then in the 12th century Peter Abelard proposed limbo, which became the standard Catholic teaching until around the council of Trent. Since then the doctrine has changed once again to what it is today.
The Catholic Church’s current position is that it is not known what happens to infants who die in infancy without baptism! Again, Catholics often deny that “Limbo” was the official teaching of the Church; but evidence suggests otherwise:
Pope Innocent III accepted Abelard’s Doctrine of Limbo, which amended Augustine of Hippo’s Doctrine of Original Sin. The Vatican accepted the view that unbaptized babies did not, as at first believed, go straight to Hell but to a special area of limbo, “limbus infantium”. They would therefore feel no pain but no supernatural happiness either (only natural) because, it was held, they would not be able to see the deity that created them. Source.