González pitching for the Cuba national team in 2013 World Baseball Classic
|Baseball World Cup|
|Pan American Games|
|2003 Santo Domingo||Team|
|2007 Rio de Janeiro||Team|
In the 2005-06 Cuban National Series, pitching alongside national team stalwarts Yosvani Pérez and Adiel Palma, González maintained a 3.97 ERA and notched 90 strikeouts in 133 innings. However, his record was only 6-10, as Cienfuegos stumbled to a 35-54 record.