In all three years he played for Bremen's youth team he finished as top scorer among the players.

[4] On 22 August 2016, he made his professional and first-team debut in Werder Bremen's first-round DFB-Pokal defeat to Sportfreunde Lotte being substituted on in place of Lennart Thy in the 62nd minute.

[5] Four days later, he scored his first professional goal in the reserves' 4–2 win against VfL Osnabrück in the 3.

[6] On 18 August 2018, Eggestein scored his first goal for the first team, in a 6–1 win against Wormatia Worms in the first round of the DFB-Pokal.

[8] On 5 October 2020, the last day of the 2020 summer transfer window, Eggestein moved to Austrian Bundesliga club LASK on loan for the 2020–21 season.