Martínez was born in 1924, in Los Angeles, California, to Mexican migrant farmworkers. In his youth, he worked with his parents harvesting crops, while harboring a desire to be an artist. In 1943, he enlisted in the United States Army and served as a unit medic in the European theatre of World War II.
Martinez participated in the Omaha Beach invasion in Normandy, France, and went on to serve in four major campaigns in Europe and received four battle stars. Shortly after returning to the U.S. in 1947, Martínez met and married Esther Silva. They had a daughter and four sons, two of whom preceded him in death.