  We have studied the viability and possible patterns of a strong first-order
electroweak phase transition (SFOEWPT) within the $Z_3$-symmetric
Next-to-Minimal Supersymmetric Standard Model (NMSSM), in view of the latest
experimental results from the dark matter (DM) sector, Higgs sector and the
searches of the lighter chargino and neutralinos at the Large Hadron Collider
(LHC). We show that the region of parameter space with relatively small
$\mu_\mathrm{eff}$ that favors an SFOEWPT has started to get excluded from the
searches at the LHC and various DM experiments. However, there still remain
phenomenologically much involved and compatible regions for an SFOEWPT that are
yet not sensitive to the latest LHC and DM searches. We further estimate the
production of stochastic gravitational waves (GW) from an SFOEWPT within and
without the bag model and the prospects of detecting such signals at various
future/proposed GW experiments.
