Montoya was born on 20 September 1975 in Bogotá, Colombia. He began karting at five, guided by his father Pablo, who refinanced the family home to fund his son's early career. After winning numerous national karting titles in Colombia through the late 1980s and early 1990s, Montoya began car racing in 1992 and moved to Europe in 1995. His early European single-seater career included the Formula Vauxhall Lotus Championship with Paul Stewart Racing in 1995, where Jackie Stewart taught him to drive with greater smoothness. In 1996 Montoya advanced to the British Formula Three Championship with Fortec Motorsport, taking two wins and finishing fifth in the championship. He also finished fourth in the Masters of Formula 3 at Zandvoort that year.
For 1997, Montoya wanted to enter the International F3000 Championship — Formula One's primary feeder series — and accepted an offer from Helmut Marko to drive for his RSM Marko squad. Marko offered guidance on fitness and diet to help Montoya adapt to the heavier F3000 machinery, though the driver's own admission was that he occasionally lacked the mental fortitude in his debut season to convert all available results. Montoya won three races driving the Lola T96/50-Zytek: at the Pau Grand Prix, the A1-Ring, and the Circuito de Jerez. He took two pole positions across the season. Errors cost him two further race victories, and he was mathematically eliminated from championship contention after finishing third in the penultimate round at Mugello, which Ricardo Zonta won. Montoya ended the season second in the Drivers' Championship with 37.5 points and was recognised as the series' highest-placed rookie.
A character clash with Marko prompted Montoya to leave RSM Marko for Super Nova Racing for 1998. Marko paid Super Nova owner David Sears for Montoya to race with the team, and Montoya declined Marko's parallel offer to become his personal manager. The season was defined by a sustained rivalry with West Competition driver Nick Heidfeld. Montoya won four races — at Circuit de Catalunya, Silverstone, the Pau Grand Prix, and the Autodromo di Pergusa — and took nine podium finishes and seven pole positions across the twelve-round calendar. He won the championship by finishing third in the season finale at the Nürburgring, ending with 65 points. Heidfeld was the closest challenger throughout, and the contest between the two drivers produced the most competitive F3000 campaign of that era.
Williams Grand Prix Engineering had invited Montoya to a shootout at the Circuit de Catalunya in November 1997 between four drivers competing for the team's F1 test driver role. Montoya won the shootout and spent 1998 covering 5,000 miles as a Williams test driver, studying telemetry for race drivers Heinz-Harald Frentzen and Jacques Villeneuve alongside his F3000 campaign. Despite having the Williams test contract, Frank Williams concluded that Montoya needed more development before a Formula One race seat and signed double CART champion Alex Zanardi in his place. Instead, Williams arranged for Chip Ganassi Racing to sign Montoya for the 1999 CART season on a three-year contract. The F3000 title was the foundation of that deal, demonstrating that Montoya could win in a competitive open-wheel series before transitioning to American open-wheel racing.
Montoya's F3000 championship is notable for its statistical completeness — four wins, nine podiums, and seven poles across twelve rounds — and for the unusual career path it enabled. Rather than moving directly from F3000 to a Formula One race seat, his Williams association redirected him toward CART, where he won the 1999 championship as a rookie, then took the Indianapolis 500 in 2000, and finally joined Williams for the 2001 Formula One season. His Formula One career produced seven race victories. The 1998 F3000 title stands as the specific credential that set this indirect but highly successful career trajectory in motion.