We report a study of the relative effects of dimensional and kinetic constraints on the stabilization of metastable, polytypic forms of metallic silver. We show that the hexagonal 4H polytype (hitherto observed only in size-constrained systems) can be produced in the form of bulk thin films by suitably slowing down the growth kinetics. Further, using extremely slow growth conditions, we have been successful in depositing a novel, two-dimensional, metastable polytype (2H) of silver, which is highly reactive (easily oxidized) and has a density 23% lower than normal silver. First-principles calculations based on density functional theory confirm that the 4H structure is relatively stable. However, local stability analysis via a determination of the phonon dispersion of the 2H structure reveals that it is only marginally stable with an energy surface that is rather flat or weakly varying with respect to many of the modes. This makes a large contribution to the configurational entropy and is probably the reason for the metastability of the observed 2H polytype with an unusually large lattice constant along the c-direction.