  We study in detail the viability and the patterns of a strong first-order
electroweak phase transition as a prerequisite to electroweak baryogenesis in
the framework of $Z_3$-invariant Next-to-Minimal Supersymmetric Standard Model
(NMSSM), in the light of recent experimental results from the Higgs sector,
dark matter (DM) searches and those from the searches of the lighter chargino
and neutralinos at the Large Hadron Collider (LHC). For the latter, we
undertake thorough recasts of the relevant, recent LHC analyses. With the help
of a few benchmark scenarios, we demonstrate that while the LHC has started to
eliminate regions of the parameter space with relatively small
$\mu_\mathrm{eff}$, that favors the coveted strong first-order phase
transition, rather steadily, there remains phenomenologically much involved and
compatible regions of the same which are yet not sensitive to the current LHC
analyses. It is further noted that such a region could also be compatible with
all pertinent theoretical and experimental constraints. We then proceed to
analyze the prospects of detecting the stochastic gravitational waves, which
are expected to arise from such a phase transition, at various future/proposed
experiments, within the mentioned theoretical framework and find them to be
somewhat ambitious under the currently projected sensitivities of those
experiments.
