Bracken was born in Astoria, Queens, New York, the son of Joseph L. and Catherine Bracken. Bracken performed in vaudeville at the age of nine and gained fame with the Broadway musical "Too Many Girls" in a role he reprised for the 1940 film adaptation. He had performed in a short film series called "The Kiddie Troupers" (one of many "Our Gang"-like series) prior to that, but that film was his big break. In 1936, Bracken enjoyed success on Broadway with his starring run in the Joseph Viertel play "So Proudly We Hail". The military drama, co-starring Richard Cromwell, opened to much fanfare but closed after 14 performances at the 46th Street Theater.