Cohen was a member of the Gumbangarri nation of the Northern Tablelands of New South Wales. His mother died when he was a boy, and his father sent him to live with his older sister. When Cohen fell out of a tree and broke his arm, he returned to live with his father. His father travelled extensively as a drover and Cohen was often left on stations to work as a milk boy, groom, and roustabout.
As a young man, Cohen became involved in street boxing. He took challenges from anyone who wanted to fight him. Upon his arrival in Newcastle, Cohen started training for boxing more officially. The managers of the boxing circuit changed his name to Maxie Williams. After leaving the boxing ring, Cohen went back to work on cattle stations.
In 1939, Cohen joined the army. During his service he was sent to Holsworthy prison camp for assaulting his NCO (Non-Commissioned Officer). After his term in the army was finished he worked on a banana plantation and on a railway gang. Later, Cohen and his wife, Esther Kelly, moved their family back to the Macleary area where he found work on the stations.
In later years, Cohen suffered from kidney complications, and ill health as a result of drinking and smoking.
(Source: Cohen, B. To My Delight : The Autobiography of Bill Cohen a grandson of the Gumbangarri, Aboriginal Studies Press, 1987)