The way of acceptance of this rebirth is twofold. The first requirement is repentance. The second step, and a natural path from the first, is to be baptized.
Historical: There is not enough information about the nature of baptism in the Book of Mormon to known whether or not Alma was speaking to those who had already been baptized or not. It is most probable that baptism was not seen as a “once in a lifetime” proposition during Book of Mormon times. The Jewish practice to which it is most similar was a full body washing that could be done at any point in one’s life where a recommitment was desired. In modern times, the idea of rebaptism as a renewal of commitment was practiced in Utah, though that practice is now discontinued.
Alma is speaking to righteous people in Gideon, and because of their righteousness, one might suppose that they had already been baptized. However, the people in Gideon were probably those who came with Limhi and Ammon. Those people were from the land of Lehi-Nephi as was Alma the Elder, but they left at different times, and Alma the Elder began his baptizing after his departure from that community. It is therefore possible that the people of Gideon might not yet have been baptized, even though they were believers in the Nephite religion and the Atoning Messiah.