The process by which a system of non-luminous bodies form around a star is fundamental to understanding the origins of our own solar system and how it fits into the context of other systems we have begun to study around other stars. Some basics of solar system formation have emerged to describe the process by which dust and gas around a newly formed star evolve into what we see today. The combination of occultation observations and the flyby observations by New Horizons of the Cold-Classical Kuiper Belt Object (CCKBO), (498958) Arrokoth, has provided essential new constraints on formation models through its three-dimensional shape. We present a case that an occultation-driven survey of CCKBOs would provide fundamental new insight into solar system formation processes by measuring population-wide distributions of shape, binarity, and spin-pole orientation as a function of size in this primordial and undisturbed reservoir.This article is part of the theme issue 'Major advances in planetary sciences thanks to stellar occultations'.