Rubuta ci gaba don wannan sakin layi - Tevez ya fara zama sananne tare da Argentina yayin wasa a 2001 FIFA U-17 Gasar Cin Kofin Duniya. A Wasannin Olympics na 2004 a Girka, ya lashe lambar zinare <unk> ta farko ta Argentina a kowane taron tun 1952 <unk> kuma ya zira kwallaye takwas a wasanni shida don zama dan wasan da ya fi kowa zura kwallo a gasar. Wannan ya hada da mai nasara a wasan karshe da Paraguay, biyu a cikin rukuni na rukuni na 6<unk>0 na Serbia da Montenegro, da kuma hat-trick a cikin nasara 4<unk>0 a wasan kusa da na karshe a kan Costa Rica. Tevez ya wakilci manyan 'yan wasan Argentina a gasar Copa América ta 2004
, inda kungiyar ta kai wasan karshe, kawai ta yi rashin nasara ga abokan hamayyar Brazil a bugun fanareti; ya ci kwallo a zagaye biyu da suka gabata. Ya kasance na biyu mafi yawan masu zura kwallaye a duniya na 2004 a cikin gasar cin kofin duniya gaba daya tare da kwallaye 16, daya kasa da dan wasan gaba na Iran Ali Daei.