Rubuta ci gaba don wannan sakin layi - González ya lashe gasar farko ta Argentina a 2003, a karkashin Marcelo Bielsa. A shekara mai zuwa an kira shi don Copa América
yayin da al'ummar ta gama na biyu, kuma ta kuma buga wasan kwallon kafa na Olympics a wasannin Olympics na 2004, inda ta lashe zinare.