Green was born on March 9, 1973 and grew up in Doubleview, a suburb of Perth, the capital of Western Australia. His family was a sporting one, with his brother Brendan eventually being selected to the professional playing staff of the West Coast Eagles Australian Rules Football team. His father Mal was also active in the game; he coached Green's junior team to three premierships.
Green participated in kickboxing and martial arts throughout his youth, in addition to his involvement in Australian Rules Football. He took up boxing at the relatively late age of 18. He and his brother had attended a clinic to assist with preparation for the next Australian Rules Football season. Noted trainer Pat Develerz convinced him that he posessed significant natural boxing ability. Green took him at his word and commenced a successful amateur career, with Develerz as his trainer.
Success at the State Amateur level led to Green being selected for an Australian Institute of Sport scholarship, with a view to development for the upcoming 1998 Commonwealth Games and the 2000 Sydney Olympics.
Green qualified for the Olympic team and got off to a dream start in the first round of the competition, stopping the Brazilian Laudelino Barros in the fourth and final round. Unfortunately, the draw wasn't favourable to him. The Russian Alexander Lebziak stopped Green in the fourth and final round of their second round bout. Lebziak went on to claim the Gold medal.