Bauer was born Esteban Ernesto Echevarría Samson, on December 2, 1956, in Havana, Cuba, the son of Lillian Samson Agostini, a schoolteacher, and Esteban Echevarría, a commercial pilot who worked for Cubana Airlines. Bauer's maternal grandfather, whose family names were Samson and Bauer, was Jewish, and immigrated to Cuba from Germany, a refugee looking to escape the devastating effects World War II and Adolf Hitler had on his safety and home country. His family immigrated from Cuba to the United States on Independence Day, 1960, when he was three years old, shortly after the end of the Cuban Revolution, settling in Miami, Florida. Once in the United States, he began using the name Steven, the English form of his given name, Esteban. He graduated from Miami Coral Park High School in 1974 and went onto study acting at Miami Dade Community College and the University of Miami, the latter where he befriended Ray Liotta.