Born in Accra, Baba moved to Spain at an early age and joined RCD Mallorca's youth setup in January 2014, from CD Leganés. He made his senior debut for the former's reserves on 29 August 2015, coming on as a second-half substitute in a 7–1 Tercera División home routing of Penya Ciutadella.
Baba scored his first senior goal on 8 May 2016, netting the opener in a 2–1 home win against CF Platges de Calvià. On 23 June, after achieving promotion, he was bought outright by the Bermellones.[2]
On 3 July 2019, after contributing with 28 matches (play-offs included) as his side achieved promotion to La Liga, Baba renewed his contract until 2022.[5] He made his debut in the category on 17 August, starting in a 2–1 home win over SD Eibar.
Baba scored his first professional goal on 31 October 2021, netting the opener in a 1–1 away draw against Cádiz CF. On 10 August 2023, he moved to fellow top tier side UD Almería in a season-long loan deal, with a buyout clause.[6]
On 4 July 2024, Almería announced the permanent signing of Baba on a three-year contract following their relegation from the top flight.[7]