Onofre initially competed in men's high jump in regional private school meets and was scouted by coaches of the Philippine athletics team becoming a candidate of for the 1958 Asian Games in Tokyo. He shifted to 100 and 200-meter runs since he felt he did inadequate in high jump and he eventually secured a berth in the men's 4x100-meter relay squad with Remigio Vista, Isaac Gomez and Claro Pellosis; all gold medalists in the 1958 Games. Onofre competing in the 4x100-meter relay won a gold medal in the 1962 Asian Games in Jakarta. A year after the games, he secured a Fulbright scholarship which enabled him to train and study in the United States. Onofre along with Vista, William Moderno, Arnulfo Valles took part 4x100-meter relay at the 1966 Asian Games in Bangkok where they settled for bronze. His last major competition was the 1968 Summer Olympics in Mexico City where he competed in men's 100-meter and 110-meter hurdles; failing to progress from the preliminaries.