Going from zero to one has very little to do with engineering management. Being able to hack out code quickly and being comfortable talking to potential customers (preferably not in that order) are the most important things and not at all related to being an EM. It's no guarantee that you'll get to hire anyone to manage.
And yeah, there are mechanically far fewer management roles than engineering roles, and since the boundary between lead engineer/first line manager is pretty porous in both directions, you're not actually competing with an equivalently smaller pool.