Marquetti was born at 277 Velarde Street, El Cerro, Havana, Cuba. He was the son of Mercedes Díaz Campos and David "El Lucumí" Marquetti Suárez, an Abakuá member of Los Chinos Buenos, a mixed band whose members dressed as Chinese. He grew up in the Havana neighborhoods of San Juan de Dios and Cayo Hueso. He started his career in 1926 with a sexteto, Minerva. He joined the Belén Puig Orchestra and the Ernesto Muñoz Conjuncto in 1930 as singer of danzons. He then joined a number of septetos, among them Septeto Cauto, led by Manuel 'Mozo' Borgella with whom he recorded in 1940 (including the song "Efi Embemoro" - the first song to be recorded; Cheo Marquetti previously had recorded this tune in a duet setting with Bienvenido Granda in 1936, accompanied by Septeto Nacional de Ignacio Piñeiro). This was followed by stints with Septeto Hatuey, Septeto Facenda and the famous Septeto Habanero. He is also said to have been a member of Septeto Cuba, Alabama de Abelardo Barroso, Jóvenes del Cayo, Dandy del 40, La Sonora Piñón and Septeto Mora.