In 2006, González moved to Deportivo Cali, making 57 appearances over two seasons. In 2007 he took a leap to Europe, joining Turkish side Çaykur Rizespor and playing 30 matches across one season. A brief spell followed at Argentina’s Huracán in 2008/09—though he did not feature—before becoming a free agent. His performances in Colombia and Turkey caught the attention of English giants Manchester City, who signed him in January 2010 following a successful trial. While González never made a first-team appearance for City, he was the reserve-team’s preferred goalkeeper during the 2010/11 season, earning plaudits for his consistency and skill. Despite this, he wasn’t included in City’s 25-man Premier League squad, marginalizing him behind established keepers like Shay Given, Stuart Taylor, Gunnar Nielsen, and later Joe Hart. By January 2011, in search of first-team minutes, González joined Championship side Leeds United on loan from Manchester City until the end of the season. He arrived on deadline day, 31 January 2011, primarily as backup to Kasper Schmeichel and Shane Higgs. While his loan was structured with a view to permanent signing should he impress, he remained unused throughout his time at Elland Road. Despite training regularly with the first team and impressing manager Simon Grayson and staff with his attitude and work ethic, González failed to claim a spot in matchday squads and made no senior appearances in competitive fixtures.

In late February, reports emerged that Manchester City might recall González to act as third-choice keeper due to injury concerns, though this never materialized, and he remained with Leeds until returning to City on 9 May 2011. His fleeting spell at Leeds underscores the precarious fortunes of loaned-out reserves seeking to break into competitive football.

Following his return, González moved on loan to Scotland’s Aberdeen in July 2011. There he finally received regular first-team football at Pittodrie, debuting against St Johnstone. He maintained the starting position until October, making 14 Scottish Premier League appearances before losing his spot. The Aberdeen loan marked a rare period of consistency in his European career.

In January 2012, González had his Manchester City contract terminated by mutual consent and signed a short-term deal with Brighton & Hove Albion, providing goalkeeper cover. He debuted for Brighton on 17 April 2012 in a 2–2 draw against Watford, going on to make four Championship appearances before departing at the end of April. Shortly after, in August 2012, he signed with Barnsley on a month-long deal to cover injuries and made four appearances in the Championship .

After his time in English football, González returned to Colombia in 2013, joining Deportivo Pasto and making four league appearances. In 2014, he moved to Águilas Doradas (Itagüí), where he featured 22 times. From 2015 until 2019, he played back at Independiente Medellín, appearing 71 times and adding more silverware—including league titles in 2016 and a Copa Colombia in 2019 . His final playing year was 2020 at Deportivo Cali, where he made 21 appearances before retiring.

Internationally, González earned two senior caps for Colombia—debuting in January 2005 against South Korea and later representing against Brazil in 2017 . Notably, he also represented his country at the 2004 Olympic qualifying tournament.

Following retirement, González transitioned into management. By June 2022, he began leading Independiente Medellín and later managed Deportes Tolima from September 2023 through 2024. In 2025, he took the managerial helm at Millonarios, one of Colombia's prominent clubs.