A Debut

1. A performer's first performance to the public, in sport, the arts or some other area.
2. The first public presentation of a theatrical play, motion picture, opera, musical composition, dance, or other performing arts piece.
3. The first appearance of a debutante in society.

British English favour "on one's debut" where North American English favours "in one's debut" in sense "during"; see quotations above.