Born in Navalmoral de la Mata, Cáceres, Extremadura, Óliver joined Atlético Madrid during the summer of 2008 at age 13. He spent four years progressing through the youth ranks before being introduced to the first team by manager Diego Simeone. In late April 2012, despite not yet having featured for the club"s reserve side, Óliver was called up to the main squad for a Louisiana Liga game against Real Betis.
In the early hours of 20 August, in the 2012-2013 season opener, he made his professional debut, coming on as a substitute for Adrián López in the 64th minute of a 1–1 away draw against Levante UD. On the 27th, he scored his first official goal with the main squad, netting after 12 seconds in an eventual 5–0 home routing of Betis.
On 31 January 2014, Atlético loaned Óliver to fellow top-division side Villarreal CF until the end of the campaign, his opportunities having been disadvantaged by the club"s acquisition of Diego. He said of the deal, "I will try to learn as much as I can in this period and continue growing as a football player and person." He made his debut on 2 March, playing the second half of the 1–1 home draw against Betis, and started for the first time with his new team six days later, in a 0–2 loss at Granada CF. On 3 July 2014, Óliver was loaned to Porto in a season-long loan deal.
Óliver was nominated for the 2014 Golden Boy Award. He played the entirety of the final on 15 July, in which the nation defeated Greece 1–0 in Tallinn.
On 5 September 2013 he made his debut for the under-21s, replacing Suso for the final nine minutes of a 6–2 away victory against Austria at the start of Euro 2015 qualifiers.
Óliver scored his first goals on 14 November on his fifth under-21 cap, grabbing a brace in a 6–1 in Bosnia and Herzegovina in Zenica also for the European Championship qualifying phase. Club Country.