The system created in high-energy heavy-ion collisions quickly reaches local equilibrium and its evolution is usually modeled with relativistic hydrodynamics. However, the effects of the early, pre-equilibrium stages of system evolution on final-state observables are largely unknown. In this work, we study the effects of pre-hydrodynamic evolution on final-state observables in various heavy-ion collision systems. We employ state-of-the art hydrodynamic simulations coupled to different pre-hydrodynamical scenarios, including Kompost, a recently-developed effective kinetic transport theory evolution model. We find that the addition of a pre-equilibrium stage can have a significant effect on the development of transverse momentum, but only a small effect on flow and fluctuations, even differentially in transverse momentum. These results impose constraints on the way in which the initial particle production immediately after the initial hard scattering is connected to the subsequent hydrodynamic evolution of the system.