Cochrane was born on 10 October 1916 in Rawene, a remote settlement in the Northland Region of New Zealand. After leaving school, he worked in his uncle's general store before enlisting in the Royal New Zealand Air Force in September 1940. By November 1941, he was flying Wellington bombers with No. 156 Squadron RAF and would complete 33 operations including the three thousand-bomber raids of Cologne. In August 1942, Cochrane was awarded an end-of-tour Distinguished Flying Cross (DFC).