 Cochrane was born on 8 August 1900 in Glasgow, where he began his football career with Shawfield Juniors.He joined Alloa Athletic in January 1922, helped them win the Division Two title and with it automatic promotion to Division One, and established a reputation as a goalscorer.Cochrane moved to England to sign for First Division club Middlesbrough for what was reported as a four-figure fee, scoring on his debut against Arsenal on 3 March 1923 to help his team to their first win of the year.