The ingredients normally required to achieve topological superconductivity (TSC) are Cooper pairing, broken inversion symmetry, and broken time-reversal symmetry. We present a theoretical exploration of the possibility of using ultra-thin films of superconducting metals as a platform for TSC. Because they necessarily break inversion symmetry when prepared on a substrate and have intrinsic Cooper pairing, they can be TSCs when time-reversal symmetry is broken by an external magnetic field. Using microscopic density functional theory calculations we show that for ultrathin Pb and $beta$-Sn superconductors the position of the Fermi level can be tuned to quasi-2D band extrema energies using strain, and that the $g$-factors of these Bloch states can be extremely large enhancing the influence of external magnetic fields.
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