Born in Camagüey, Cuba, Sosa began studying marimba at the age of eight, then switched to piano at the Escuela Nacional de Musica in Havana, where he studied jazz. Sosa moved to Quito, Ecuador, in 1993, then San Francisco, California, in 1995. In San Francisco he became deeply involved in the local Latin jazz scene and began a long collaboration with percussionist John Santos. He also made a series of recordings with producer Greg Landau, including the ground-breaking Oaktown Irawo, featuring Tower of Power drummer Dave Garibaldi, Cuban saxophonist Yosvany Terry and Cuban percussionist Jesus Diaz. Sosa and Landau recorded with Carlos "Patato" Valdes and Pancho Quinto and worked on several film scores. Around 1999 Sosa moved to Barcelona, Spain.
Annually performing more than 100 concerts on six continents, Omar has appeared in many of the most famous venues like the Blue Note (New York, Milan, and Tokyo), London's Barbican and Queen Elizabeth Hall, Glasgow's Royal Concert Hall and many more.