Many technologically critical materials are metastable under ambient conditions, yet the understanding of how to rationally design and guide the synthesis of these materials is limited. This work presents an integrated approach that targets a metastable lead-free piezoelectric polymorph of SrHfO₃ . First-principles calculations predict that the previous experimentally unrealized, metastable P4mm phase of SrHfO₃ should exhibit a direct piezoelectric response (d₃₃ ) of 36.9 pC N^-1 (compared to d₃₃ = 0 for the ground state). Combining computationally optimized substrate selection and synthesis conditions lead to the epitaxial stabilization of the polar P4mm phase of SrHfO₃ on SrTiO₃ . The films are structurally consistent with the theory predictions. A ferroelectric-induced large signal effective converse piezoelectric response of 5.2 pm V^-1 for a 35 nm film is observed, indicating the ability to predict and target multifunctionality. This illustrates a coupled theory-experimental approach to the discovery and realization of new multifunctional polymorphs.