  We extend our previous investigation of the effects of pre-hydrodynamic
evolution on final-state observables in heavy-ion collisions to smaller
systems. We use a state-of-the-art hybrid model for the numerical simulations
with optimal parameters obtained from a previous Bayesian study. By studying
p-Pb collisions, we find that the effects due to the assumption of a conformal
evolution in the pre-hydrodynamical stage are even more important in small
systems. We also show that this effect depends on the time duration of the
pre-equilibrium stage, which is further enhanced in small systems. Finally, we
show that the recent proposal of a free-streaming with subluminal velocity for
the pre-equilibrium stage, thus effectively breaking conformal invariance, can
alleviate the contamination of final state observables. Our study further
reinforces the need for moving beyond conformal approaches in pre-equilibrium
dynamics modeling, especially when extracting transport coefficients from
hybrid models in the high-precision era of heavy-ion collisions.
