Two years after Garcia was born, Cuba became embroiled in revolution, and in January 1959 Fidel Castro assumed power in that country. Garcia's father lost his property as a result of Castro's confiscation of land from private owners. In 1961 the U.S. government backed an invasion of Cuba by anti-Castro forces. That invasion effort failed and caused many Cuban residents to flee to Spain or the U.S. for safety. In the midst of this political turmoil, when Garcia was five years old, he and his family moved to Miami, Florida. Once in Miami, Garcia attended the local high school, where he played basketball for a time. After contracting mononucleosis, which he believed dulled his athletic edge, he discovered acting. He went on to study acting at Florida International University and performed in regional theater productions until 1978.
Like many other struggling actors who dream of stardom, Garcia was attracted to Hollywood, the hub of the movie industry. In 1978 he moved to what he referred to Hollywood. He worked as a waiter to earn a living while he auditioned for parts. In 1980 he secured a role with an improvisational group at the Comedy Store in Los Angeles. It was there that a casting agent for the television series Hill Street Blues spotted him. That discovery enabled him to land a role as a gang member in the pilot episode of the show in 1981. That same year, Garcia married Maria Victoria, a Cuban American, with whom he has had three children.
In 1983 Garcia made his film debut in Blue Skies Again, a movie about baseball. That was followed in 1984 with The Mean Season, while in 1985 Garcia appeared in Eight Million Ways To Die. His big break came in 1987 when he landed a significant role in the blockbuster film The Untouchables, which starred Kevin Costner. Garcia, who played a cop-turned-government agent in the film, received his first critical acclaim for acting. The next year, he appeared in Blood Money: The Story of Clinton and Nadine, an original HBO film. He also appeared in American Roulette, a spy thriller, and Stand and Deliver.