Mezue ahịrịokwu na-esonụ: González mere egwuregwu mbụ ya maka Costa Rica na May 1990 na egwuregwu ọkụ ọkụ megide Poland, n'ihu 1990 FIFA World Cup na Italy. N'ebe ahụ, mgbe ọ dị afọ 19, o nyere otu goolu megide Czechoslovakia, na-aghọ onye ọkpụkpọ kasị nta nke nyere goolu na World Cup ahụ. O nwetara ngụkọta nke 65 caps, na-eburu 5 ihe mgbaru ọsọ ma na-anọchite anya mba ya na 19 FIFA World Cup qualification matches na na 1991 CONCACAF Gold Cup nakwa na
1993 na 1997 UNCAF Nations Cups. Ọzọkwa, ọ bụ onye isi obodo ya n'oge 1997 Copa América ma bụrụ onye otu na-abụghị egwuregwu na 2001 Copa América.