Pedzisa mutsara unotevera: González akaita kutanga kwake kuCosta Rica mumutambo waNovember 2002 wekushamwaridzana 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.