  Advances in the control of intense infrared light have led to the striking
discovery of metastable superconductivity in $\mathrm{K}_3\mathrm{C}_{60}$ at
100K, lasting more than 10 nanoseconds. Inspired by these experiments, we
discuss possible mechanisms for long-lived, photo-induced superconductivity
above $T_{c}$. We analyze a minimal model of optically-driven Raman phonons
coupled to inter-band electronic transitions. Using this model, we develop a
possible microscopic mechanism for photo-controlling the pairing interaction by
displacively shifting the Raman mode. Leveraging this mechanism, we explore two
pictures of long-lived, light-induced superconductivity far above $T_c$. We
first investigate long-lived, photo-induced superconductivity arising from the
metastable trapping of a displaced phonon coordinate. We then propose an
alternate route to long-lived superconductivity. Within this paradigm, the slow
equilibration of quasi-particles enables a long-lived, non-thermal
superconducting gap. We conclude by discussing implications of both scenarios
to experiments that can be used to discriminate between them. Our work provides
falsifiable, mechanistic explanations for the nanosecond scale photo-induced
superconductivity found in $\mathrm{K}_3\mathrm{C}_{60}$, while also offering a
theoretical basis for exploring long-lived, non-equilibrium superconductivity
in other quantum materials.
