  Using hybrid molecular dynamics/SWAP Monte Carlo (MD/SMC) simulations, we
show that the terminal relaxation times $\tau$ for FIRE energy minimization of
soft-sphere glasses exhibit thermal onset as samples become increasingly
well-equilibrated. Although $\tau(\phi)$ can decrease by orders of magnitude as
equilibration proceeds and the jamming density $\phi_{\rm J}$ increases via
thermal onset, it always scales as $\tau(\phi) \sim (\phi_{\rm J} - \phi)^{-2}
\sim [Z_{\rm iso} - Z_{\rm ms}(\tau)]^{-2}$, where $\phi_{\rm J}$ is the
jamming density and $Z_{\rm ms}(\tau)$ is the average coordination number of
particles satisfying a minimal local mechanical stability criterion ($Z \geq
d+1$) at the top of the final potential-energy-landscape (PEL) sub-basin the
system encounters. This scaling allows us to collapse $\tau$ datasets that look
very different when plotted as a function of $\phi$, and to address a closely
related question: how does the character of the PEL basins that dense thermal
glasses most typically occupy evolve as the glasses age at constant $\phi$ and
$T$?
