Kammala wannan jumla: Kostitsyn ya yi wasan sa na biyu na 'yan kasa da shekaru 20 a gasar
2002 Gasar Hockey ta Junior ta Duniya kuma ta zira kwallaye uku don taimakawa Belarus ta kasance a cikin manyan rukuni. Daga baya a waccan shekarar, Kostitsyn ya koma babban rukuni a 2002 IIHF World U18 Championship, inda ya zira kwallaye 10 a wasanni takwas kuma ya taimaka ya jagoranci Belarus zuwa na biyar. Kasancewa a gasarsa ta uku a karkashin 20 a gasar zakarun duniya na hockey na matasa na 2003, Kostitsyn ya zira kwallaye biyu da taimako daya, amma an sauke shi tare da Belarus zuwa Division-I a shekara ta 2004. Yin wasa a mataki na biyu, ya zira kwallaye biyar da maki 10 a wasanni biyar don taimakawa Belarus ta koma babban rukuni a shekara ta 2005, inda ya zira kwallaye biyar a karo na biyar da na karshe na Junior na Duniya.