Cohen played four years of college soccer at the University of California, San Diego between 2010 and 2013, graduating with a degree in bioengineering and computer science.[6] He appeared in 51 games in his collegiate career. In 2012, he started 12 games and led the entirety of NCAA Division II in goals against average (0.397) and save percentage (0.898), earning a place on the Daktronics All-America Second Team. In 2013, he started 22 games and earned NSCAA All-America First Team honors.[7]
In early 2014, Cohen was invited by the Philadelphia Union to a one-week trial from January 25 through February 1.[8]
Burlingame Dragons
After college, Cohen appeared for USL PDL side Burlingame Dragons in 2015, making 11 appearances with a goals against average of 0.636.[9]
Cohen spent the 2017 season with Phoenix Rising where he won the starting goalkeeper role, making 28 starts on the season. He earned the September 2017 Player of the Month Award with a 0.37 GAA and 88.9% save percentage over the course of the month.[13]
Sacramento Republic
Cohen signed with Sacramento Republic FC of the USL Championship on January 16, 2018, with a club option for 2019.[14] He played every minute of the 2018 USL Championship season, conceding 32 goals in the 34 games of the regular season, and earning twelve clean sheets. Cohen was named a finalist for USL Goalkeeper of the Year[15] and was selected to the USL All-League Second Team.[16]
He returned to Sacramento for the start of the 2019 season and made 16 appearances, allowing just 17 goals, before his transfer.[citation needed]
Maccabi Haifa
On July 19, 2019, Sacramento Republic and Maccabi Haifa agreed to a transfer of Cohen to the Israeli Premier League club in advance of their 2019–20 season.[17] Cohen made his first start on September 25, 2019, where he was in net for a 3–0 victory over Maccabi Netanya. He returned to the starting line-up on October 26, 2019, for another 3–0 victory, this time over Hapoel Kfar Saba. He then started every game until the season's eventual postponement. In that time, he conceded only 15 goals in his 21 games, saw out 12 clean sheets, and helped lead Maccabi Haifa to a second-place finish at the end of the first stage of the regular season.[18]
In the 2021–22 season, Cohen led the club to repeat as Israeli Premier League Champions, finishing the season with the best defensive record in the league and earning 16 clean sheets across the campaign. This earned Maccabi Haifa a 2022-23 UEFA Champions League playoff round berth, where they would go on to defeat Olympiacos, Apollon Limassol, and Red Star Belgrade.[20] In the ensuing UCL group stage, Cohen's five saves led Haifa to a 2–0 clean sheet win over Juventus.[21]
In May 2023, Cohen and Haifa clinched their third consecutive Israeli Premier League title with a 5–1 win over Maccabi Netanya.[22]