Born in Tczew, Kuzimski began his career with Unia Tczew, but suffered a knee injury in his early 20s. After moving to England to work in a food packing warehouse, he attended a trial for uncontracted players, and after a second trial signed for Cambridge City F.C., before moving to Histon F.C. He played 30 times for Histon, scoring four goals, before returning to Poland with Bałtyk Gdynia.