Rosa Cuthbert was born in 1922 in Diego Martin, on the Caribbean island of Trinidad. She and her younger sister Ameze were left with relatives when their parents Audrey and Henry Cuthbert emigrated in 1927 to the United States. The children did not join their parents in Harlem until 1932. The following year their mother became ill, and Rosa and her sister were sent to Brooklyn to live with a cousin. Her espousal of Garveyism and black nationalistic politics deeply affected Rosa. After their mother's death in 1934, the two girls returned to Harlem to live with their father, who remarried.
When he died in 1937, the girls were orphaned. After that, they were taken into the welfare system and lived in foster homes. Rosa left school at the age of 14 and took a job in a garment factory to support herself and her sister.
In 1941 at the age of 19, Rosa met and married Warner Guy. While her husband was serving in the Second World War she continued working in the factory. A co-worker introduced her to the American Negro Theatre, where she studied acting; other graduates included Harry Belafonte and Sidney Poitier. In 1942, her son Warren Guy, Jr, was born.
After the war, Rosa Guy moved to Connecticut with her husband and son. Five years later she and her husband divorced, and she returned to New York.