We should start with a sustainable colony _on_ earth as a proof of concept. :-)

Only a madman would get onto a generation ship on a one-way non-abandonable non-rescuable trip without seeing the proof of a sustainable colony orbiting the earth first.

Given the acceleration and (eco)system bring-up challenges, I suspect it would take more than one generation from "keel laying" to the ship first leaving the solar system. You'd have a generation living in a partly-constructed colony ship while building the rest of it.