Born in Nguidile, Louga Region, Thiam left for Italy at young age. Thiam was selected to Veneto region Allievi team for Coppa Nazionale Primavera, a competition against other Italy regional representatives in 2007–08 season. At club level he played for Real San Marco, from Chirignago, mainland area of Venice municipality. In 2008, he was signed by Veneto club Treviso. In January 2009 he was signed by Internazionale from Treviso along with Samuel Longo. He immediately entered Inter's Allievi Nazionali under-17 team, scoring 4 goals in regular season (group stage). Due to Inter's Primavera under-20 team had many strikers, namely Denis Alibec, Mattia Destro, Simone Dell'Agnello, Giuseppe Angarano and Longo, Thiam left for Sassuolo's Primavera team (literally Spring team) in August 2009. The Emilia-Romagna side also borrowed Alberto Gallinetta and kept numbers of former Inter players by extended the loans or excised the option to sign outright from Inter, such as Pellegrino Albanese, Raffaele Conforto and Giorgio Schiavini. Thiam was the starting forward along with Diego Falcinelli, who also from Inter academy. However the coach also used other formation and preferred Falcinelli as sole centre forward despite Thiam also played that role few time. That season Thiam scored 4 times.
During the season, Inter formed a complex deal with Sassuolo, which allowed Thiam to join Sassuolo for free in January 2010 (Inter registered a loss of €71,000), then Thiam re-joined Inter on 30 August in co-ownership deal, with Thiam's contract treated as a financial asset in Sassuolo's account and an intangible asset in Inter account, as well as the "parent" club of the co-ownership contract became Sassuolo instead of Inter. With Inter "Spring", he scored 4 goals in the regular season, behind strikers Dell'Agnello, Alibec and midfielder Milan Jirásek. He also won 2011 Torneo di Viareggio with the reserves.
On 30 August 2011 he left for Avellino. Thiam made his professional debut on 25 September (round 4), substituted Gianluca De Angelis. He made his first start in the next game, partnering Gianmarco Zigoni (round 5). He played the successive game, scoring on 13, 16 and 30 October (round 7, 8 and 10), partnering Zigoni, Fabrizio Lasagna and De Angelis respectively. However, after a goal drought Thiam lost the starting place, and became the backup of De Angelis and Zigoni. He returned to starting XI again on 7 March 2012, partnering Zigoni. In June 2012 Inter also acquired Thiam outright, as Sassuolo gave up their 50% registration rights of Thiam.
On 12 July 2012 Thiam was signed by another third level club South Tyrol (German: Südtirol, Italian: Alto Adige).
On 15 July 2013, Thiam joined Serie B club Lanciano on a free transfer. On 30 January 2014, Lanciano signed goalkeeper Laurențiu Brănescu in a co-ownership deal for €250,000 cash plus 50% registration rights of Thiam (50% "card" of Thiam was valued at €1.4 million; 50% "card" of Brănescu was valued €1.65 million). Thiam signed a 4½-year contract with The Old Lady.
Thiam spent the rest of the 2013–14 season in Lanciano. He continues in Lanciano in the 2014–2015 season. In June 2015 Juventus signed Thiam outright for another €800,000; on 8 July Lanciano signed Filippo Penna (about €340,000) and Marco Di Benedetto (undisclosed) as compensations.
On 26 July 2015 Zulte Waregem signed Thiam in a temporary deal. The move made Juventus had a signing quota for non-European Union nationals (another quota was from Carlos Tevez), which the club later signed Alex Sandro, who counted as a non-EU.
After the loan Thiam returned to Juventus for their pre-season camp.
On 31 August 2016 PAOK signed Thiam in a temporary deal.
On 13 January 2017 Empoli signed Thiam in a temporary deal. He scored a goal against A.C. Milan on 23 April 2017, giving Empoli a crucial 3-points for their battle from relegation. He also played in the last round of the season, which Empoli relegated by losing to already relegated Palermo.
After the loan, Thiam returned to Turin once again for their pre-season camp.