  The ongoing LIGO-Virgo-KAGRA observing run O4 provides an opportunity to
discover new multi-messenger events, including binary neutron star (BNS)
mergers such as GW170817, and the highly anticipated first detection of a
multi-messenger black hole-neutron star (BH-NS) merger. While BNS mergers were
predicted to exhibit early optical emission from mildly relativistic outflows,
it has remained uncertain whether the BH-NS merger ejecta provides the
conditions for similar signals to emerge. We present the first modeling of
early near-ultraviolet/optical emission from mildly relativistic outflows in
BH-NS mergers. Adopting optimal binary properties: a mass ratio of $q=2$ and a
rapidly rotating BH, we utilize numerical relativity and general relativistic
magnetohydrodynamic (GRMHD) simulations to follow the binary's evolution from
pre-merger to homologous expansion. We use an M1 neutrino transport GRMHD
simulation to self-consistently estimate the opacity distribution in the
outflows and find a bright near-ultraviolet/optical signal that emerges due to
jet-powered cocoon cooling emission, outshining the kilonova emission at early
time. The signal peaks at an absolute magnitude of $\sim -15$ a few hours after
the merger, longer than previous estimates, which did not consider the first
principles-based jet launching. By late 2024, the Rubin Observatory will have
the capability to track the entire signal evolution or detect its peak up to
distances of $\gtrsim1$ Gpc. In 2026, ULTRASAT will conduct all-sky surveys
within minutes, detecting some of these events within $\sim 200$ Mpc. The BH-NS
mergers with higher mass ratios or lower BH spins would produce shorter and
fainter signals.
