In 2011 he moved to FC Zürich, and signed his first professional contract with the club in 2014. While he was initially promised playing time in the first team, he was used sparingly at the club, and for that reason Oberlin sought to transfer away from the club. He was sought after by Manchester United in England, but would've started in their academy with the Under-18 team. For that reason, Oberlin chose to transfer to Red Bull Salzburg in Austria, where a path to the first team was clearer. Oberlin was often compared with fellow Cameroon-born, Swiss international Breel Embolo, and Zürich chairman Ancillo Capella remarked upon Oberlin's departure that he did not want "hysterical mothers claiming that their sons are at least as good as Embolo".
Salzburg
On 30 June 2015, Red Bull Salzburg made the announcement that they had signed a three-year contract with Oberlin. Oberlin scored his first goal with Salzburg in his second game with the club, against Rapid Wien on 1 August, after coming on as a second-half substitute. He ended up splitting his first season with Salzburg and their farm club, Liefering. He scored three goals with Salzburg, and seven with Liefering in the Erste Liga. Oberlin received an offer from Red Bull parent club RB Leipzig in the German Bundesliga, but declined, citing the importance of playing first team football.
Oberlin was loaned out to fellow Austrian Football Bundesliga club Rheindorf Altach for the 2016–17 season. Oberlin got off to an amazing start with Altach, as he scored 6 goals in his first 5 games with the club. He finished the first half of the season with 9 goals, second in the league to Deni Alar, as Altach were the surprise leaders of the league at the halfway point of the season. Oberlin was recalled by RB Salzburg at that point, and he found the back of the net on his first match back, scoring the only goal in a 1–0 win over Mattersburg. He made three more appearances before missing nearly two months with a muscle tear in his thigh, picked up while on international duty with the Swiss under-20 team. Expected to miss the rest of the season, Oberlin returned in time to make a substitute appearance against his former club that season, Altach, in the final game. Altach were in fourth by that point in the season, and Salzburg won 1–0 as they ran away with the championship, their fourth in a row.
Basel
On 20 June 2017, FC Basel announced that they had acquired Oberlin on loan from Salzburg, with the option of a definite transfer. Basel, as champions of the Swiss Super League the previous year, earned a spot in the group stage of the Champions League. Oberlin appeared as a substitute against Manchester United at Old Trafford, but started for Basel against Portuguese club Benfica. On 27 September 2017, Oberlin played in the starting eleven in the Champions League Group stage match against Benfica. Basel ran out 5–0 victors at St. Jakob-Park, with Oberlin scoring two goals and assisting a third, highlighted by his full-field sprint after heading away a Benfica corner to finish off a Basel counter-attack with a goal. Oberlin made 4 starts in the group stage, scoring 4 goals as Basel advanced to the knockout stages, second in their group behind Manchester United. Drawn against Manchester City, Basel lost 5–2 on aggregate, but they did defeat City in the second leg in Manchester 1–2, as Oberlin started both legs. He also scored on his debut with the club in the league on 5 August, finishing off a 3–0 victory over Thun with his stoppage time goal. Under trainer Marcel Koller Basel won the Swiss Cup in the 2018–19 season. In the first round Basel beat FC Montlingen 3–0, in the second round Echallens Région 7–2 and in the round of 16 Winterthur 1–0. In the quarter finals Sion were defeated 4–2 after extra time and in the semi finals Zürich were defeated 3–1. All these games were played away from home. The final was held on the 19 May 2019 in the Stade de Suisse Wankdorf Bern against Thun. Striker Albian Ajeti scored the first goal, Fabian Frei the second for Basel, then Dejan Sorgić netted a goal for Thun, but the end result was 2–1 for Basel. Oberlin played in four cup games and scored a goal in the semi-final against Zürich.
Empoli
On 31 January 2019, the last day of the 2018–19 winter transfer window, Oberlin moved to Serie A side Empoli F.C. on loan for the season with Empoli securing an option to make the signing permanent.
Oberlin received his first call to the Switzerland national football team for friendlies against Greece and Panama in March 2018. Born in Cameroon, Oberlin moved to Switzerland at the age of 9, and has participated in their youth ranks from the age of 14. He made his debut on 23 March 2018 in a game against Greece.
