Topological materials are derived from the interplay between symmetry and topology. Advances in topological band theories have led to the prediction that the antiperovskite oxide Sr$_3$SnO is a topological crystalline insulator, a new electronic phase of matter where the conductivity in its (001) crystallographic planes is protected by crystallographic point group symmetries. Realization of this material, however, is challenging. Guided by thermodynamic calculations we design and implement a deposition approach to achieve the adsorption-controlled growth of epitaxial Sr$_3$SnO single-crystal films by molecular-beam epitaxy (MBE). In-situ transport and angle-resolved photoemission spectroscopy measurements reveal the metallic and non-trivial topological nature of the as-grown samples. Compared with conventional MBE, the synthesis route used results in superior sample quality and is readily adapted to other topological systems with antiperovskite structures. The successful realization of thin films of topological crystalline insulators opens opportunities to manipulate topological states by tuning symmetries via epitaxial strain and heterostructuring.