Kammala jumla mai zuwa: Kostitsyn ya wakilci Belarus sosai a matakin Under-18 da -20. Ya fara wasa a duniya a 2000 IIHF World U18 Championships yana ɗan shekara goma sha biyar, amma Belarus za ta yi gwagwarmaya a babban rukuni, ta gama ƙarshe. A shekara mai zuwa, Kostitsyn ya yi gasa tare da tawagar 'yan kasa da shekaru 20 na Belarus a gasar cin kofin duniya.
2001 Gasar Hockey ta Junior ta Duniya 'babban rukuni. Daga baya a wannan shekarar, bayan da aka sauke shi don 2001 IIHF World U18 Championships, Kostitsyn ya dawo don yin rikodin gasar da ke jagorantar maki 14 a wasanni biyar a cikin rukuni na biyu don lashe gasar zakarun Turai na Division I.