Jossa was born in Bexley. She trained at D&B Theatre School in Bromley (where she performed the role Jeanie in 'Hair' to great acclaim), followed by the Royal Academy of Music in London. At music college her activities included performing the Bruch violin concerto. She has one older sister, Katrina and her two older brothers died in infancy. She is the cousin of former EastEnders actress Megan Jossa. She is half Irish from her mother who moved to England before Jossa was born.