  Several Pulsar Timing Array (PTA) collaborations have recently provided
strong evidence for a nHz Stochastic Gravitational-Wave Background (SGWB). Here
we investigate the implications of a first-order phase transition occurring
within the early universe's dark quantum chromodynamics (dQCD) epoch,
specifically within the framework of the mirror twin Higgs dark sector model.
Our analysis indicates a distinguishable SGWB signal originating from this
phase transition, which can explain the measurements obtained by PTAs.
Remarkably, a significant portion of the parameter space for the SGWB signal
also effectively resolves the existing tensions in both the $H_0$ and $S_8$
measurements in Cosmology. This intriguing correlation suggests a possible
common origin of these three phenomena for $0.2 < \Delta N_{\rm eff} < 0.5$,
where the mirror dark matter component constitutes about $30\%$ of the total
dark matter abundance. Next generation CMB experiment such as CMB-S4 is able to
test this parameter region.
