  With some explicitly $Z_3$ breaking terms in the NMSSM effective
superpotential and scalar potential, domain walls (DWs) from spontaneously
breaking of the discrete symmetry in approximate $Z_3$-invariant NMSSM can
collapse and lead to observable stochastic gravitational wave (GW) background
signals. In the presence of a hidden sector, such terms may originate from the
geometric superconformal breaking with holomorphic quadratic correction to
frame function when the global scale-invariant superpotential is naturally
embedded into the canonical superconformal supergravity models. The smallness
of such mass parameters in the NMSSM may be traced back to the original
superconformal invariance. Naive estimations indicate that a SUSY explanation
to muon $g-2$ anomaly can have tension with the constraints on SUSY by PTA
data, because large SUSY contributions to $\Delta a_\mu$ in general needs
relatively light superpartners while present $\Omega_{gw}^0$ can set the lower
bounds for $m_{soft}$. We calculate numerically the signatures of GW produced
from the collapse of DWs and find that the observed nHZ stochastic GW
background by NANOGrav, etc., can indeed be explained with proper tiny values
of $\chi m_{3/2}\sim 10^{-14}{\rm eV}$ for $\chi S^2$ case (and $\chi
m_{3/2}\sim 10^{-10}{\rm eV}$ for $\chi H_u H_d$ case), respectively. Besides,
there are still some parameter points, whose GW spectra intersect with the
NANOGrav signal region, that can explain the muon $g-2$ anomaly to $1\sigma$
range.
