Self-propelled colloidal objects, such as motile bacteria or synthetic microswimmers, have microscopically irreversible individual dynamics-a feature they share with all living systems. The incoherent behavior of individual swimmers can be harnessed (or "rectified") by microfluidic devices that create systematic motions that are impossible in equilibrium. We present a computational proof-of-concept study showing that such active rectification devices could be created directly from an unstructured "primordial soup" of light-controlled motile particles, solely by using spatially modulated illumination to control their local propulsion speed. Alongside both microscopic irreversibility and speed modulation, our mechanism requires spatial symmetry breaking, such as a chevron light pattern, and strong interactions between particles, such as volume exclusion, which cause a collisional slowdown at high density. Together, we show how these four factors create a novel, many-body rectification mechanism. Our work suggests that standard spatial light modulator technology might allow the programmable, light-induced self-assembly of active rectification devices from an unstructured particle bath.