  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.
