Oshilaja began his career in the youth academy of Cardiff City, where he progressed through the ranks and eventually made his first-team debut in 2014. During his time at Cardiff, Oshilaja also had loan spells at lower league clubs such as Newport County, Sheffield Wednesday, and AFC Wimbledon. He eventually signed a permanent deal with AFC Wimbledon in 2017, where he established himself as a key player in the defense.