Rubuta ci gaba don wannan sakin layi - González ya fara buga wasan farko na kasa da kasa don tawagar Venezuela a ranar 23 ga Janairu, 1993, a wasan da suka yi da Peru 0<unk>0. Ya wakilci al'ummar a cikin bugu uku na Copa América (1993
, 1995 da 1997), kuma ya shafe shekaru goma sha ɗaya ba tare da buga wa kungiyar wasa ba har zuwa wasan sa na karshe a 2008.