das Debüt
debut
The first public appearance of an artist, athlete, or group.
Die junge Pianistin feierte gestern ihr Debüt mit dem Philharmonischen Orchester.
The young pianist made her debut with the Philharmonic Orchestra yesterday.

debut
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debut
The first public appearance of an artist, athlete, or group.
Die junge Pianistin feierte gestern ihr Debüt mit dem Philharmonischen Orchester.
The young pianist made her debut with the Philharmonic Orchestra yesterday.

'Debüt' (debut) is a loanword from French and is therefore often used in cultural or artistic contexts. It sounds more formal and more specific than 'erster Auftritt' (first appearance).
Das Debüt des jungen Regisseurs wurde auf dem Filmfestival gefeiert.
The young director's debut was celebrated at the film festival.
When referring to an appearance, 'Debüt' (debut) is very frequently combined with the verbs 'geben' (to give/make), 'feiern' (to celebrate), or 'haben' (to have).
Der Stürmer gab sein Debüt in der Nationalmannschaft.
The striker made his debut on the national team.
When referring to a first work, 'Debüt-' (debut) is often used as the first part of compound nouns. Examples are 'Debütroman' (debut novel), 'Debütalbum' (debut album), or 'Debütfilm' (debut film).
Ihr Debütroman handelt von einer Reise durch Asien.
Her debut novel is about a journey through Asia.
performance / appearance
'der Auftritt' and 'das Debüt' can both refer to a public performance, for example on a stage or in sports. The important difference is: 'der Auftritt' can be any individual appearance before an audience, even if the person has been well known for a long time. 'das Debüt' is only the first public appearance of a person or group. Learners may confuse the words because a debut can always also be an Auftritt. But not every Auftritt is a debut. When it is about doing something 'for the first time', 'Debüt' fits; otherwise, 'Auftritt' is usually the better choice.

Die junge Sängerin feiert morgen ihr Debüt auf der großen Bühne.
The young singer makes her debut on the big stage tomorrow.
Der Auftritt der Band beginnt heute Abend um acht Uhr.
The band's performance starts tonight at eight o'clock.