Gough was born on 28 February 1980. Born in Wexford and raised in Ennis, County Clare, Gough is the seventh of eleven siblings; her father was variously an electrician and a fisheries head, while her mother was a marriage counsellor. One of her younger sisters is the actress Kelly Gough. Gough was raised as a Catholic.
She trained as a soprano before leaving Ireland for London at 15, with a boyfriend, after which she became homeless for a while. She started using alcohol and drugs to block out the experience of being groomed from the age of 13 and raped twice at 14 by "a man in his 20s"; "At the time [Gough] thought it was love", but she later realised that she had been the victim of child abuse.
She was awarded a grant to study at the Academy of Live and Recorded Arts (ALRA) in Wandsworth aged 18, and graduated from ALRA in 2003.