Kammala jumla mai zuwa: González ya fara bugawa tawagar kasar Venezuela wasa a ranar 23 ga Janairu, 1993, a wasan da suka yi da Peru. 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.