 Nyorai kuenderera mberi kweiyi ndima - Kostitsyn akaita kechipiri pasi pemakore makumi maviri ku2002 World Junior Ice Hockey Championships uye akarova zvibodzwa zvitatu kubatsira Belarus kugara muchikamu chepamusoro. Gare gare gore iroro, Kostitsyn akadzokera kuchikwata chepamusoro pa2002 IIHF World U18 Championships, achiwana mapoinzi gumi mumitambo misere uye achibatsira kutungamira Belarus kunzvimbo yechishanu. Achikwikwidza mumutambo wake wechitatu pasi pemakore makumi maviri pamakwikwi eWorld Junior Ice Hockey Championships muna 2003, Kostitsyn akarekodha zvibodzwa zviviri uye rubatsiro rumwe, asi akadzikiswa neBelarus kuDivision-I muna 2004. Achitamba muchikamu chechipiri, akarova zvibodzwa zvishanu uye mapoinzi gumi mumitambo mishanu kubatsira Belarus kudzokera kuchikamu chepamusoro muna 2005, kwaakarova mapoinzi mashanu muWorld Juniors yake yechishanu uye yekupedzisira. 