Kammala jumla mai zuwa: González ya lashe kofinsa na farko ga Argentina a 2003, a karkashin Marcelo Bielsa. A shekara mai zuwa sai aka kira shi don
Copa América a matsayin al'umma ta gama na biyu, kuma ta kuma buga wasan ƙwallon ƙafa a wasannin Olympics na 2004, inda ta lashe zinare.