  The induced gravitational wave (GW) background from enhanced primordial
scalar perturbations is one of the most promising observational consequences of
primordial black hole (PBH) formation from inflation. We investigate the
induced GW spectrum $\Omega_{\textrm{IGW}}$ from single-field inflation in the
general ultra-slow-roll (USR) framework, restricting the peak frequency band to
be inside $10^{-3}$-$1$ Hz and saturating PBH abundance to comprise all dark
matter (DM) in the ultralight asteroid-mass window. By invoking successful
baryogenesis driven by USR inflation, we verify the viable parameter space for
the specific density ratio between baryons and PBH DM observed today, the
so-called "cosmic coincidence." We show that the cosmic coincidence requirement
bounds the spectral index $n_{\rm UV}$ in the high frequency limit,
$\Omega_{\textrm{IGW}}(f\gg 1)\propto f^{-2n_{\rm UV}}$, into $0 < n_{\rm UV} <
1$, which implies that baryogenesis triggered by USR inflation for PBHs in the
mass range of $10^{-16}$-$10^{-12} M_\odot$ can be tested by upcoming Advanced
LIGO and Virgo data and next generation experiments such as LISA, Einstein
Telescope, TianQin and DECIGO.
