。
She made her debut as a musician.
Literal
She [topic-は] musician [as-として] for-the-first-time world [to-に] came-out.
世に出る — literally 'come out into the world' — is the idiomatic Japanese expression for making one's professional debut, breaking into a field, or first becoming known to the public. The image is of stepping out from private obscurity onto a public stage. ~として ('as / in the capacity of') labels the role under which she emerged: not as just any person, but specifically as a musician. 初めて ('for the first time') marks the inaugural quality of the act.