Damase was born in Bordeaux, the son of harpist Micheline Kahn.[2] He was studying piano and solfège with Marcel Samuel-Rousseau at the age of five and composing by age nine.[3] His first work (at the age of nine) was a setting of some poems by Colette, whom he had met at a Parisian salon.[1] In 1940, Damase began studying piano with Alfred Cortot at the École Normale de Musique.[4] The next year, he was admitted to the Conservatoire de Paris, entering Armand Ferté’s piano classes[4] and winning first prize for piano in 1943,[3] afterwards studying with Henri Büsser, Marcel Dupré and Claude Delvincourt for composition[3] and winning first prize for composition in 1947 for his Quintet for flute, harp, violin, viola, and cello.[4] In the same year, he won the Grand Prix de Rome[5] for his cantata Et la belle se réveilla.[4] Meanwhile, he appeared as a piano soloist in the Colonne and Conservatoire concerts, and with the Orchestre National of the ORTF.[4]
He made the first complete recording of Gabriel Fauré's nocturnes and barcarolles, for which he received the Grand Prix du Disque.[6]