 Following his schooling at Sydney Boys High School in the 1920s, Thicknesse was a half-back with Sydney's Eastern Suburbs Rugby Union Club.He switched to the professional code in 1931 and joining Eastern Suburbs' rugby league side.He was a member of the Tricolours' champion teams of the 1930s and won consecutive premierships with the club in the seasons of 1935, 1936 and NSWRL season 1937.