Prior to the start of his racing career, Alcaraz enjoyed a long and illustrious karting career which began in the year 2000, when he won the Spanish District Championship Catalonia title. He followed that up a year later with victory in the Copa Campeones Trophy Cadet class. He raced primarily in his homeland until 2004, when he began to take part in various European karting championships such as the European Championship ICA Junior, Andrea Margutti Trophy ICA Junior and Italian Open Masters ICA Junior categories.
2005 saw Alcaraz claim the Spanish Championship ICA Junior title, beating countryman Roberto Merhi by four points, and finish third in the Andrea Margutti Trophy ICA Junior class, behind Merhi and Charles Pic. His final year of karting in 2006 saw Alcaraz claim fifth place in the World Cup ICA class.
In October 2006, Alcaraz stepped up to single-seaters, racing in the penultimate round of the Spanish Formula Three Championship season in Jerez, where he finished the two races in 16th and 15th places respectively.
Later the same month, Alcaraz made his Formula Renault début at the final round of the Eurocup Formula Renault 2.0 season in Barcelona, finishing the two events in 24th and 23rd place respectively. In November 2006, he took part in the Italian Formula Renault 2.0 Winter Series for Cram Competition, finishing in 7th place with team-mate and current Formula One driver Jaime Alguersuari winning all four races and the title.
In 2007, Alcaraz contested both the Eurocup Formula Renault 2.0 and Italian Formula Renault 2.0 series with the Petrom District Racing AP team, alongside Mihai Marinescu. In the Eurocup he finished in 19th place after two points finishes, whilst in the Italian championship he finished in the points on eight occasions to be classified in 17th place, despite missing the final round of the series at Monza.
In November 2007, Alcaraz sampled a Formula Renault 3.5 Series car for the first time, driving for Pons Racing at the opening winter test at Paul Ricard. Although he conducted the majority of his winter testing with the team, he was signed by Italian team RC Motorsport to contest the 2008 season. Despite an encouraging start to the season, when he finished in the points in only his second race, he left the team after the fourth round of the year at Silverstone and was subsequently replaced by Brazilian Claudio Cantelli.
Alcaraz did, however, return to the series at the following round of the season in Hungary, taking the seat of Máximo Cortés at Pons Racing, who had run into sponsorship problems. In his ten races for the team, he took a single points finish in the sprint race at Le Mans to eventually be classified 27th in the final standings.
† - As Alcaraz was a guest driver, he was ineligible to score points.
(key) (Races in bold indicate pole position) (Races in italics indicate fastest lap)