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The advent of sensitive gravitational wave (GW) detectors, coupled with wide-field, high cadence optical time-domain surveys, raises the possibility of the first joint GW-electromagnetic (EM) detections of core-collapse supernovae (CCSNe). For targeted searches of GWs from CCSNe optical observations can be used to increase the sensitivity of the search by restricting the relevant time interval, defined here as the GW search window (GSW). The extent of the GSW is a critical factor in determining the achievable false alarm probability (FAP) for a triggered CCSN search. The ability to constrain the GSW from optical observations depends on how early a CCSN is detected, as well as the ability to model the early optical emission. Here we present several approaches to constrain the GSW, ranging in complexity from model-independent analytical fits of the early light curve, model-dependent fits of the rising or entire light curve, and a new data-driven approach using existing well-sampled CCSN light curves from {\it Kepler} and the Transiting Exoplanet Survey Satellite (TESS). We use these approaches to determine the time of core-collapse and its associated uncertainty (i.e., the GSW). We apply our methods to two Type II SNe that occurred during LIGO/Virgo Observing Run 3: SN\,2019fcn and SN\,2019ejj (both in the same galaxy at $d=15.7$ Mpc). Our approach shortens the duration of the GSW and improves the robustness of the GSW compared to techniques used in past GW CCSN searches.