Baena scored his first professional goal on 5 November 2020, netting his team's third in a 4–0 UEFA Europa League home routing of Maccabi Tel Aviv FC.[6] Seven days later, he renewed his contract until 2025.[7]
On 19 August 2021, Baena moved to Segunda División side Girona FC on a one-year loan deal.[8] He returned to the Yellow Submarine after being a starter in the Catalans' promotion, and scored a brace in a 3–0 away win over Real Valladolid on 13 August 2022.
On 26 August 2022, Baena and teammate Nicolas Jackson were fully promoted to the main squad.[9] In the 2023–24 season, he became the top assist provider in La Liga with 14 assists.[10]
^"Álex Baena, la 'perla' que brilla en el filial" [Álex Baena, the 'pearl' who shines in the reserves] (in Spanish). El Periódico Mediterráneo. 3 October 2019. Archived from the original on 2 November 2020. Retrieved 13 July 2020.