Physical vapor deposition can produce remarkably stable glassy materials. However, a mechanistic understanding of the interplay between control parameters during such nonequilibrium processing (e.g., deposition rate, substrate temperature, incident velocity, etc.) remains an unresolved challenge to date. In this study, we report on the discovery of a dual role of incident molecules' mass-center velocity in controlling the stability of vapor-deposited glasses through atomistic modeling. On one hand, larger velocities would impose the surface atoms into a higher effective temperature environment and facilitate the relaxation as the sample approaches the glass transition temperature. On the other hand, larger velocities would meanwhile cause faster cooling rates for the deposited molecules and destabilize the sample. The competition between the two factors results in a remarkable nonmonotonic variation of the sample's stability where an optimal velocity can be quantitatively resolved. Implications of our findings for better controlling molecular-level mechanisms in glassy materials are discussed.