First, a reminder about “scriptural foundation”: To speak of the Catholic faith as “based” in Scripture is pure anachronism. The Church herself wrote the New Testament, and canonized the Old Testament. The Church had been expanding throughout the world for more than three centuries before she established the canon of Scripture. In the New Testament, the Church enshrined key elements of the Gospel, but not its entirety. Read again John 21:25. The Catholic faith, therefore, cannot be “based” in Scripture, but it is reflected in Scripture.
We are all born with original sin; what the Council of Trent called “death of the soul.” That is the reason the Church baptizes even infants who have no personal sins. We want our newborns to be incorporated into the Mystical Body of Christ at the earliest possible time. The fact that grace is purely a gift is most clearly demonstrated in baptizing infants.
Consider this: When a child is born of American parents, the child receives a great gift, American citizenship. In order to exercise that gift the child will need instruction for mature citizenship. But never will the child be more of a citizen than at the moment of birth. By analogy we can say that the infant becomes a Christian at the moment of baptism. Yet that infant will need nurture for the rest of his or her life to grow in sanctity. The Acts of the Apostles refers to baptism of households (see 16:15), which presumably included young children, even infants. Beginning in the second century, there is clear testimony to infant baptism as an immemorial tradition of the Church.