The doctrine of baptismal regeneration is one of those doctrines that is so clear and explicit in the Bible that, even using a sola scriptura hermeneutic, it can easily be defended. For a discussion of some key texts and issues, see, for instance:
John Greer vs. the biblical doctrine of baptismal regeneration
Christ's baptism is NOT imputed to the believer
Such is also the case for the Book of Mormon, wherein the instrumental cause of one’s initial justification and one’s regeneration is that of water baptism. In Alma 19:35-36, water baptism is presented as the instrumental cause of one’s justification (being made [not merely “declared”] righteous) and the beginning of one’s salvation, something reminiscent of the theology of Acts 2:37-39:
And it came to pass that there were many that did not believe in their words; and as many as did believe were baptized; and they became a righteous people, and they did establish a church among them. And thus the work of the Lord did commence among the Lamanites; thus the Lord did begin to pour out his Spirit upon them; and we see that his arm is extended to all people who will repent and believe on his name.