Design systems do not make the first version faster. They make the fortieth change cheaper — which is a very different sales pitch.
There is a myth that a design system speeds up the initial build. It does not. Building tokens, documenting components and agreeing naming all cost time you could have spent shipping screens.
The payoff arrives later, on the change nobody planned for.
So the question is never "do we need a design system". It is "how many times will this interface change after launch". If the answer is once or twice, skip it. If the answer is continuously, start on day one.