Núñez-Juárez was born in San Sebastián, Puerto Rico, where he received his primary and secondary education. In 1952, Núñez-Juárez was inducted into the Marines in San Juan, the island's capital, and reported to Marine Corps Recruit Depot Parris Island, South Carolina. After he graduated from his basic training, he was sent to Camp Lejeune in North Carolina where he underwent advanced training before being sent to Korea. He was assigned as an automatic rifleman to Company E of the 2nd Battalion, 1st Marines (2/1), 1st Marine Division.