Ku qor sii wadida cutubkan - Kostitsyn wuxuu markii labaad u soo muuqday ciyaar ka yar 20 sano ee Koobka Hockeyga Barafka ee Koobka Adduunka ee 2002
waxaana uu dhaliyay seddex gool si uu ugu caawiyo Belarus in ay sii joogaan horyaalka. Kadib sanadkaas, Kostitsyn wuxuu ku soo laabtay horyaalka ugu sarreeya ee 2002 IIHF World U18 Championships, isagoo diiwaan galiyay 10 dhibcood siddeed ciyaarood wuxuuna gacan ka geystay hoggaaminta Belarus si uu u dhammeeyo kaalinta shanaad. Kostitsyn wuxuu ka qeyb galay tartankiisii saddexaad ee ka hooseeya 20 ee 2003 World Junior Ice Hockey Championships, wuxuu diiwaan geliyay laba gool iyo hal caawin, laakiin wuxuu la galay Belarus ilaa Division-I 2004. Isaga oo ka ciyaaraya heerka labaad, wuxuu dhaliyay shan gool iyo 10 dhibcood shan kulan si uu uga caawiyo Belarus inay ku soo laabato horyaalka ugu sareeya 2005, halkaas oo uu ka dhaliyay shan dhibcood kulankiisii shanaad iyo kii ugu dambeeyay ee World Juniors.