Born in Hankow, China, Crosbie grew up in Glasgow and attended the Glasgow School of Art between 1932 and 1935 where he was awarded a travel scholarship and visited Paris, studying under Modernists Ferdinand Léger and Aristide Maillol. Returning to the UK, Crosbie continued to create artwork throughout the war while serving the in the Merchant Navy. In 1946, he held his first exhibition in London’s Lefevre Gallery alongside Surrealist painter John Armstrong and during this time grew in popularity through creating altarpieces, book illustrations and murals including for the Festival of Britain,1951.