Rubuta ci gaba don wannan sakin layi - González ya fara buga wasan farko na Costa Rica a watan Mayu 1990 a wasan motsa jiki da Poland, kafin gasar cin kofin duniya ta 1990 a Italiya. A can, yana da shekaru 19, ya zura kwallo a wasan da suka yi da Czechoslovakia, ya zama dan wasa mafi ƙanƙanta da ya zura kwallo a gasar cin kofin duniya. Ya sami adadin wasanni 65, inda ya zira kwallaye 5 kuma ya wakilci kasarsa a wasanni 19 na gasar cin kofin duniya na FIFA da kuma a gasar cin kofin zinare ta CONCACAF ta 1991 da kuma a gasar cin kofin duniya ta 1993.
da kuma 1997 UNCAF Nations Cups. Har ila yau, ya kasance kyaftin din kasarsa a lokacin Copa América na 1997 kuma ya kasance dan wasan da ba ya wasa a gasar Copa América ta 2001.