Rubuta ci gaba don wannan sakin layi - Kostitsyn ya yi wasan sa na biyu a karkashin 20 a Gasar Hockey ta Duniya ta 2002
kuma ya zura kwallaye uku don taimakawa Belarus ta ci gaba da kasancewa a cikin rukunin farko. 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 don 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.