  Supposing the Laser Interferometer Space Antenna (LISA) gravitational wave
(GW) detector, we exhibit the detectability of a hypothetical smooth crossover
in the early universe beyond the Standard Model of particle physics through the
scalar-induced gravitational wave (SIGW) in terms of the Fisher forecast. A
crossover at $\sim100\,\mathrm{TeV}$ can leave a signal on the GW spectrum in
the $\sim\mathrm{mHz}$ frequency range, the sweet spot of the LISA sensitivity.
These possibilities are also interesting in the primordial black hole (PBH)
context as the associated PBH mass $\sim10^{22}\,\mathrm{g}$ lies at the window
to explain the whole dark matter. We found that the properties of the crossover
can be well determined if the power spectrum of primordial scalar perturbations
are as large as $\sim5\times10^{-4}$ on the corresponding scale
$\sim10^{12}\,\mathrm{Mpc^{-1}}$.
