  Light new physics weakly coupled to the Higgs can induce a strong first-order
electroweak phase transition (EWPT). Here, we argue that scenarios in which the
EWPT is driven first-order by a light scalar with mass between $\sim 10$ GeV -
$m_h/2$ and small mixing with the Higgs will be conclusively probed by the
high-luminosity LHC and future Higgs factories. Our arguments are based on
analytic and numerical studies of the finite-temperature effective potential
and provide a well-motivated target for exotic Higgs decay searches at the LHC
and future lepton colliders.
