Data for paper 'Terahertz Emission Mediated for Ultrafast Time-Varying Metasurfaces', appearing in Physical Review Research (2021).Systems with ultrafast time-varying dielectric properties represent an emerging novel physical framework. We demonstrate here the first observation of sub-cycle dynamics interacting directly with an electromagnetic source comprised of morphologically constrained photoexcited carriers in a surface nanostructure. A transition to a metallic metasurface state occurs on time scales faster than the Terahertz-field period, inducing large nonlinear ultrafast phase shifts in the Terahertz emission and exposing a novel and previously unexplored physical setting