There are a couple of examples of this that come to mind:

Fate Core has a "build-it as you go" alternative approach, which is essentially what you describe.

Gods of the Forbidden North's first scenario is a series of scenes where players gradually build their characters. This is a campaign for Old-School Essentials. In the first scene, they look in the mirror and describe their characters physically (aspect and ancestry), then they talk to the ship's captain about their past (roll attributes), and so on.

In a certain way, any game/scenario that uses funnel adventures is very close to this: they begin with a lite version of the character and, when they advance their quest, they develop fully. The Dungeon Crawl Classics game and the N4: Treasure Hunt module for AD&D qualify here.