Gonzalez akaita mutambo wake wekutanga kuCosta Rica munaNovember 2002 mumutambo wehushamwari neEcuador uye akawana huwandu hwe61 caps, achiwana 1 chinangwa. Akamirira nyika yake mumitambo gumi nemashanu yeFIFA World Cup uye akatamba pa2006 FIFA World Cup pamwe ne2003, 2007
uye 2009 CONCACAF Gold Cups. Akasarudzwawo kuti atambe muUNCAF Nations Cup 2007, kwaakarova zvibodzwa vachipesana neHonduras.