Briscoe was born in Alice Springs. He is descended from the Marduntjara and Pitjantjatjara nations of Central Australia. He was taken away from his mother as a child and was taught at a Christian mission in Adelaide. Briscoe played football (soccer) for Adelaide in the South Australian league. He played alongside his schoolmate Charles Perkins. In 1958, he moved to England with the hope of playing professional football. He had small jobs with Barnet and Preston North End, but he did not make a first team appearance. He went back to Australia at the suggestion of Perkins. The two of them later played recreational football with the Australian National University from 1968 to about 1972.