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 ultrathin 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 -Sn superconductors, the position of the Fermi level can be tuned to quasi-2D band extrema energies using strain, and that the factors of states at time-reversal invariant momenta can be extremely large, enhancing the influence of external magnetic fields.