  In this paper, the collider signature of the heavy Higgs boson at $14$ TeV
HL-LHC is studied, where heavy Higgs boson decays into a pair of standard model
Higgs boson, which further decays to $bbZZ$ state and subsequently to
$bb\ell^{+} \ell^{-}\nu_{\ell} \nu_{\ell}$ final state. To study this, we
consider singlet scalar extension of the standard model and considered the
parameter space and mass of the heavy Higgs such that it prefers the strong
first order electroweak phase transition. The study is done following the
$bbZZ$ analysis of CMS Collaboration and further using parameterized machine
learning for final discrimination which simplifies the training process along
with an improved discrimination between signal and background over the range of
benchmark points. Despite the lower branching fractions, this channel can be a
potential probe of the electroweak phase transition with the data sets
collected by the CMS and ATLAS experiments in the $14$ TeV HL-LHC with $3$
$\rm{ab}^{-1}$ of integrated luminosity and a production of resonant di-Higgs
signal can be potentially discovered.
