Díaz joined the choir of the University of Puerto Rico, under the direction of Augusto Rodríguez, where he sang solo. His operatic debut was in 1957 as Ben in Gian Carlo Menotti's "The Telephone, or L'Amour à trois". It wasn't long before Díaz enrolled in New England Conservatory in Massachusetts. One of his professors was Boris Goldovsky, who would be very influential in his career. Díaz made his professional debut as an opera singer at the Opera Theater of New England. In 1960, Goldovsky asked Díaz to join his opera company on a 20-state tour. After the tour, he entered and participated in a competition celebrated at the Metropolitan Opera House, winning third place in the New England region.