González has won nine medals (four golds, four silvers, and one bronze) at World Cup events, six medals (one gold, three silvers, and two bronzes) at Pan American Games, seven medals (two golds, two silvers, and three bronzes) at South American Games and one gold medal at the January 2012 London Olympics test event (where he qualified for the Olympics). He has participated in eight World Championships (2003, 2005, 2007, 2009, 2010, 2011, 2015, and 2017), finishing 7th in 2009, 6th in 2011, 8th in 2015, and 5th in 2017 on floor, and 15th in 2010 and 22nd in 2011 in individual all-around.