We employ an effective kinetic description, based on the Boltzmann equation in the relaxation time approximation, to study the space-time dynamics and development of transverse flow of small and large collision systems. By combining analytical insights in the small opacity limit with numerical simulations at larger opacities, we are able to describe the cooling due to longitudinal expansion and development of transverse flow from very small to very large opacities. Our results demonstrate that for large opacities, the system follows a Bjorken flow scaling law up to intermediate times. In comparing transverse flow, surprisingly, we find that deviations between kinetic theory and hydrodynamics persist even in the limit of very large opacities, which can be attributed to the presence of the early pre-equilibrium phase.