Córdoba signed with the St. Louis Cardinals as an international free agent on April 12, 2013. He made his professional debut with the DSL Cardinals in 2013, and also played for the club in 2014, hitting .272 and .258 respectively. He was the Gulf Coast League Most Valuable Player (MVP) in 2015 after hitting .342 in 53 games, and won the Appalachian League batting title while playing with a .362 batting average with the Johnson City Cardinals in 2016. With Johnson City, he made 220 plate appearances, batted .362, .427 on-base percentage, 16 doubles and five triples.
Córdoba was selected by the San Diego Padres after the season in the 2016 Rule 5 draft.
Córdoba made the Padres' 2017 Opening Day roster. At 21 years old, he had never previously played above Rookie League ball. He hit his first major league home run on April 18, 2017, versus Jaime García in the seventh inning of 5−4 loss to the Atlanta Braves at SunTrust Park. Córdoba was batting as high as .310 as of June 2, but he slumped afterward, and lost playing time as a result. Cordoba made a total of 42 starts in 2017, 24 in left field, 15 at shortstop, 2 in center, and 1 in right, but only had 56 plate appearances after the All-Star break. Cordoba made 11 of his starts in left in May after Travis Jankowski went down with a foot injury, but he was displaced by José Pirela, who came up in early June. He saw more playing time at shortstop in June, but the Padres chose to stay with Erick Aybar, and then Dusty Coleman when Aybar was on the disabled list. Cordoba finished the season with a .208/.282/.297 batting line and 4 home runs in 202 at-bats.

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