On 12 November 2019, after graduating from Oxford United's academy, Goodrham made his debut for the club in a 4–1 EFL Trophy win against Crawley Town, becoming Oxford's youngest ever player in the process, aged 16 years and 98 days.[2] In September 2021 he had his first senior loan when he joined Southern Football League Premier Division South side Hayes & Yeading United.[3] He was recalled on 18 November after a successful loan spell with Hayes reaching the first round of the FA Cup and the team challenging at the top of the table.[4]
Goodrham made his League One debut for Oxford as a late substitute against Cambridge United on 6 August 2022 and scored the winning goal in injury time.[6]