Garza was born in 1948 in Kingsville, Texas. She is the second of five children. This small community is near the Mexico-United States border. Garza loved watching her mother paint, and felt like what her mother did was magic. Garza had also seen her mother painting picture cards for a game that is similar to Bingo around the time she was 8, which increased her love of art even more. Garza wanted to be an artist from the time she was thirteen when she started drawing every day. Garza helped her grandmother create embroidery patterns using paper cutouts as a young child. The influence of her mother's and grandmother's art-making was very strong and by age thirteen Garza had decided she would be an artist. Her parents encouraged her to pursue her interests in college.