  We investigate the prospective reach of the 14 TeV HL-LHC for resonant
production of a heavy Higgs boson that decays to two SM-like Higgs bosons in
the $4b$ final state in the scalar singlet extended Standard Model. We focus on
the reach for choices of parameters yielding a strong first order electroweak
phase transition. The event selection follows the $4b$ analysis by the ATLAS
Collaboration, enhanced with the use of a boosted decision tree method to
optimize the discrimination between signal and background events. The output of
the multivariate discriminant is used directly in the statistical analysis. The
prospective reach of the $4b$ channel is compatible with previous projections
for the $bb\gamma\gamma$ and $4\tau$ channels for heavy Higgs boson mass $m_2$
below 500 GeV and superior to these channels for $m_2 > 500$ GeV. With 3
ab$^{-1}$ of integrated luminosity, it is possible to discover the heavy Higgs
boson in the $4b$ channel for $m_2< 500$ GeV in regions of parameter space
yielding a strong first order electroweak phase transition and satisfying all
other phenomenological constraints.
