González began in karting before entering the 2003 Formula Renault 2.0 UK Winter Series. He raced in the main Formula Renault 2.0 UK Championship in 2004 and 2005 while attending City College Norwich.
In 2006 he won the British F3 International Series National Class competing for T-Sport — his clearest single-season domestic success at the junior level. He remained with T-Sport for 2007, finishing eleventh in the British Formula 3 Championship. For 2008 he moved to Carlin Motorsport and the more competitive Formula Three Euro Series, where the season proved difficult; he accumulated just half a championship point, scored in a rain-shortened sprint race at Le Mans.
González first appeared in the GP2 Asia Series in 2008–09, replacing Andreas Zuber for the third round at Sakhir. He finished sixteenth on debut and ended the Asia Series 23rd in the standings, with eighth in a Sepang sprint race as his best result.
He made a brief main-series GP2 entry in 2009 as a replacement for Davide Rigon at Trident Racing for the German rounds. He also competed in Euroseries 3000 that year, finishing fifth overall.
For the 2009–10 GP2 Asia Series, González raced for Arden International at the opening round before being replaced. He returned for the Bahrain finale substituting for Sergio Pérez at Barwa Addax. In the 2010 GP2 Series proper he partnered Charles Pic at Arden, scoring four points and finishing 21st in the championship.
In 2011 González moved to Trident Racing for the GP2 Asia Series and main series, partnering Stefano Coletti. He finished seventeenth in the Asia series and 26th in the main championship. He then signed with Caterham Racing alongside Giedo van der Garde for 2012, ending the season 22nd in the championship.
In late 2010, González participated in the young driver test at Abu Dhabi driving the Lotus T127, alongside Bulgarian Vladimir Arabadzhiev.
On 14 March 2013, Marussia F1 announced González as the team's reserve driver for the 2013 Formula One season. He drove in Friday practice sessions at the Hungarian, Italian, and Korean Grands Prix for Marussia. The Korean outing ended with a crash that drew attention to the difficulty of his role within a backmarker operation.
González competed in the 2014 European Le Mans Series Championship with the Murphy Prototypes Endurance Racing Team in the LMP2 category. He also participated in the 2014 Le Mans Classic.
González tested IndyCar machinery in the 2014–15 off-season, sampling cars with both Schmidt Peterson Motorsports and Dale Coyne Racing. He made a surprise IndyCar debut at Barber Motorsports Park in 2015, the fourth round of the season, entered in the Dale Coyne No. 18 car. He then ran five further races that year, achieving a best finish of ninth at the Sonoma Raceway season finale.
After a period away from competition, González returned in 2023, announced to drive for Idola Motorsport in the Britcar Prototype Cup in a Praga R1 alongside Ruben Stanislau. He won the opening race of the season at Silverstone.
González's career reflects the path of a well-travelled South American driver navigating the European and American single-seater ladders across a decade and a half. His reserve and practice roles with Marussia brought him to the Formula One paddock without a race start, while his IndyCar appearances and endurance outings kept him active across multiple disciplines. The 2023 Silverstone Britcar victory marked a late-career return to winning form.
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