noun, noun which may take the genitive case particle 'no'
first time in one's life
Used to describe an experience or event that is happening for the very first time in a person's life. Often used attributively with の or as a noun.
I'm going on my first overseas trip ever.
It was a first-in-a-lifetime experience.
Compound of 人生 (life) and 初 (first). The exact origin is uncertain, but it is a straightforward modern coinage.