We analyze a sample of 45 Type II supernovae from the Zwicky Transient Facility public survey using a grid of hydrodynamical models in order to assess whether theoretically driven forecasts can intelligently guide follow-up observations supporting all-sky survey alert streams. We estimate several progenitor properties and explosion physics parameters, including zero-age main-sequence (ZAMS) mass, mass-loss rate, kinetic energy, 56Ni mass synthesized, host extinction, and the time of the explosion. Using complete light curves we obtain confident characterizations for 34 events in our sample, with the inferences of the remaining 11 events limited either by poorly constraining data or the boundaries of our model grid. We also simulate real-time characterization of alert stream data by comparing our model grid to various stages of incomplete light curves (Δt < 25 days, Δt < 50 days, all data), and find that some parameters are more reliable indicators of true values at early epochs than others. Specifically, ZAMS mass, time of the explosion, steepness parameter β, and host extinction are reasonably constrained with incomplete light-curve data, whereas mass-loss rate, kinetic energy, and 56Ni mass estimates generally require complete light curves spanning >100 days. We conclude that real-time modeling of transients, supported by multi-band synthetic light curves tailored to survey passbands, can be used as a powerful tool to identify critical epochs of follow-up observations. Our findings are relevant to identifying, prioritizing, and coordinating efficient follow-up of transients discovered by the Vera C. Rubin Observatory.