Named after the French socialist Gustave Hervé, she was born in Florence, where she attended a convent school. At the age of ten, however, she and her family left Italy for the United States, settling in Pittsburgh, Pennsylvania, where she later studied at the Pittsburgh Music Institute. In 1948, Nelli sang in Genoa (La Gioconda, conducted by Tullio Serafin) and at the Teatro alla Scala. At the latter theatre, she participated in the Boito Memorial Concert (excerpts from Mefistofele and Nerone, conducted by Toscanini) and starred in eight performances of Aida (with Elena Nicolai as Amneris).