Alvin Baca was born to Angela and Antonio Baca of Santa Clara Pueblo in 1966. Like his siblings, David and Leona, he learned the traditional craft of pottery making from their mother. He specializes in red and black melon jars, jars with bear paw imprints and "beehive" pots (jars with horizontal polished ribs).

Alvin was an exhibitor at the Santa Fe Indian Market from 1988 to 1999, earning a Third Place ribbon for an undecorated melon jar in 1994. He was also an exhibitor at the Eight Northern Pueblos Arts and Crafts Show from 1994 to 1999.