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 shekarar 2008.