Resolving the early-stage dynamics of exciton formation following non-resonant photoexcitation in time, energy, and momentum is quite challenging due to their inherently fast timescales and the proximity of the excitonic state to the bottom of the conduction band. In this study, by combining time- and angle-resolved photoemission spectroscopy with ab initio numerical simulations, we capture the timing of the early-stage exciton dynamics in energy and momentum, starting from the photoexcited population in the conduction band, progressing through the formation of free excitons, and ultimately leading to their trapping in lattice deformations. The chosen material is bismuth tri-iodide (BiI3), a layered semiconductor with a rich landscape of excitons in the electronic structure both in bulk and in monolayer form. The obtained results, providing a full characterization of the exciton formation, elucidate the early stages of the physical phenomena underlying the operation of the ultrafast semiconductor device.