Yunost Minsk
Beginning in 2000–01, Kostitsyn spent the first two seasons of his early career with Polimir Novopolotsk, competing in several leagues, including the Eastern European Hockey League (EEHL). In the summer of 2002, he signed with CSKA Moscow and moved to Russia. He split his time with the organization between CSKA 2 of Russia's developmental league, and also continued to play in the Belarusian league with Yunost Minsk.