O'Keefe was born and raised in Blackley, in the city of Manchester. He went to school with Mike Pickering, who later found fame as a musician. As a youth he was a ball boy at Old Trafford, and was on course to join the Manchester United youth team when he broke his leg in a collision with David Allison, son of Malcolm Allison, in a regional schoolboy game. Upon his recovery he joined Stalybridge Celtic of the Cheshire County League, and playing as a right-back he won the club's Player of the Year award. This won him a chance in the Football League, and he turned down Crystal Palace to instead sign with Third Division club Plymouth Argyle in February 1974. He was told by manager Tony Waiters that he would never be anything more than a fringe player in the professional game, who then allowed him to leave Home Park on a free transfer. He returned to Manchester and signed with Hyde United for the 1974–75 Cheshire County League season.