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.