High quality Van der Waals chalcogenides are important for phase change data storage, thermoelectrics, and spintronics. Using a combination of statistical design of experiments and density functional theory, we clarify how the out-of-equilibrium van der Waals epitaxial deposition methods can improve the crystal quality of Sb2Te3 films. We compare films grown by radio frequency sputtering and pulsed laser deposition (PLD). The growth factors that influence the crystal quality for each method are different. For PLD grown films a thin amorphous Sb2Te3 seed layer most significantly influences the crystal quality. In contrast, the crystalline quality of films grown by sputtering is rather sensitive to the deposition temperature and less affected by the presence of a seed layer. This difference is somewhat surprising as both methods are out-of-thermal-equilibrium plasma-based methods. Non-adiabatic quantum molecular dynamics simulations show that this difference originates from the density of excited atoms in the plasma. The PLD plasma is more intense and with higher energy than that used in sputtering, and this increases the electronic temperature of the deposited atoms, which concomitantly increases the adatom diffusion lengths in PLD. In contrast, the adatom diffusivity is dominated by the thermal temperature for sputter grown films. These results explain the wide range of Sb2Te3 and superlattice crystal qualities observed in the literature. These results indicate that, contrary to popular belief, plasma-based deposition methods are suitable for growing high quality crystalline chalcogenides.