Paget was born in Denver, Colorado, one of five children born to Margaret Allen (née Gibson), a former Actress (one source says, "ex-burlesque queen"), and Frank Henry Griffin, a Painter. The family moved from Denver to Los Angeles, California, in the 1930s to be close to the developing film industry. Paget was enrolled in the Hollywood Professional School when she was 11. Margaret was determined that Debra and her siblings would also make their careers in show Business. Three of Paget's siblings, Marcia (Teala Loring), Leslie (Lisa Gaye), and Frank (Ruell Shayne), entered show Business.