Thiam started his senior footballing career in 2012 in Hungary with Kaposvári Rákóczi, making 25 appearances and scoring 4 goals in two years with the Nemzeti Bajnokság I team; he also played 13 times for the team's reserves in the second tier Nemzeti Bajnokság II.[1] In 2014, Thiam joined fellow Hungarian top-flight club MTK Budapest and subsequently made his debut on 26 July in a league match against Pécsi MFC.[1] 47 appearances and 3 goals in his first two seasons came prior to him leaving MTK to complete a loan move to Major League Soccer club Chicago Fire on 4 May 2016.[2] He scored one goal, vs. Philadelphia Union, in twenty games in the United States before returning to Hungary.[1]
On 25 January 2017, Thiam joined Süper Lig side Gaziantepspor on a three-and-a-half-year contract.[3]
On 21 August 2017, Russian club FC Dynamo Moscow announced the signing of Thiam on a one-year loan deal from MTK Budapest (as Gaziantepspor did not activate a buyout option). The Dynamo contract included a buyout option.[4] The loan was terminated on 12 February 2018 by mutual consent after Thiam failed to establish his position in the Dynamo squad.[5]
On 14 February 2018, he was loaned to the Bulgarian club Levski Sofia until the end of the season.[6] On 2 June 2018, Thiam was permanently transferred to Levski, where he established himself as a regular starter. On 28 June 2020, he captained the team in the 2:1 away win over Beroe in a First League game, which had been announced beforehand to be his last match for the "bluemen".[7]
In August 2020 Thiam joined Turkish club Altay.[8] In July 2022, Thiam joined Pendikspor[9] where he remained until December 2022.[10]
On 31 January 2023, Thiam returned to MTK Budapest, now in the second-tier NB II. He signed a two-and-a-half-year contract.[11]
In an interview for Hungarian media in July 2019, Thiam announced he had sent his documents for a Hungarian passport since he moved to the country at age 18 and his wife, with whom they have two kids, is also Hungarian, and he also showed a desire to represent Hungary at international level.[12]