González began in karting before entering the Formula Renault 2.0 UK Winter Series in 2003, then raced in the main UK Formula Renault championship in 2004 and 2005 while studying at City College Norwich.
He moved to British Formula Three with T-Sport in 2006, winning the National Class championship that year. In 2007 he continued with T-Sport, finishing eleventh overall in the British F3 standings. A step up to the Formula Three Euroseries in 2008 with Carlin Motorsport proved difficult, amassing just half a point across the season.
González entered GP2 Asia series competition in late 2008, joining the main field in 2009 as a replacement driver for Trident Racing at the German rounds. He raced in the GP2 Asia Series for Arden International at the start of the 2009–10 season before being replaced, then returned at the Bahrain finale substituting for Sergio Pérez at Barwa Addax.
A full GP2 season with Arden in 2010 alongside Charles Pic yielded four points and 21st in the standings. He moved to Trident Racing for 2011 alongside Stefano Coletti, finishing 26th in the main series and 17th in the Asia series. For 2012, Caterham Racing signed him alongside Giedo van der Garde, and he ended that season 22nd in the standings.
In 2010, González drove the Lotus T127 at the Abu Dhabi end-of-season young driver test alongside Bulgarian Vladimir Arabadzhiev.
On 14 March 2013, Marussia F1 announced González as reserve driver for the 2013 Formula One season. He drove in three practice sessions that year, at the Hungarian, Italian, and Korean Grands Prix. The Korean session was particularly notable as he crashed during the session.
González tested IndyCar machinery in the 2014–15 off-season with Schmidt Peterson Motorsports and Dale Coyne Racing. He made a surprise entry into the IndyCar Series at the fourth round of the 2015 season at Barber Motorsports Park in Dale Coyne's No. 18 car. He ran five further races that year, achieving a best finish of ninth at the season-ending race at Sonoma Raceway.
In 2014, González raced in the European Le Mans Series with the Murphy Prototypes Endurance Racing Team in the LMP2 category and also participated in the 2014 Le Mans Classic.
In 2023, González was announced as a driver for Idola Motorsport in the Britcar Prototype Cup, racing a Praga R1 alongside Ruben Stanislau. He won the opening race of the season at Silverstone.
González represents a generation of drivers who used European single-seater ladders as a route toward Formula One but ultimately found themselves serving in support roles rather than race seats. His Marussia reserve appointment provided genuine F1 programme proximity, while his IndyCar participation later demonstrated willingness to pursue competitive opportunities across different categories and continents.