González made his senior debut for Costa Rica in a May 1990 warm-up match against Poland, just ahead of the 1990 FIFA World Cup in Italy. There, at 19 years of age, he scored a goal against Czechoslovakia, becoming the youngest player to score a goal in that World Cup. He earned a total of 65 caps, scoring 5 goals and represented his country in 19 FIFA World Cup qualification matches and at the 1991 CONCACAF Gold Cup as well as at the 1993 and 1997 UNCAF Nations Cups. Also, he was his country's captain during the 1997 Copa América and was a non-playing squad member at the 2001 Copa América.