  Post-starburst galaxies (PSBs) are young quiescent galaxies that have
recently experienced a rapid decrease in star formation, allowing us to probe
the fast-quenching period of galaxy evolution. In this work, we obtained HST
WFC3/F110W imaging to measure the sizes of 171 massive
($\mathrm{log(M_{*}/M_{\odot})\sim\,11)}$ spectroscopically identified PSBs at
$1<z<1.3$ selected from the DESI Survey Validation Luminous Red Galaxy sample.
This statistical sample constitutes an order of magnitude increase from the
$\sim20$ PSBs with space-based imaging and deep spectroscopy. We perform
structural fitting of the target galaxies with \texttt{pysersic} and compare
them to quiescent and star-forming galaxies in the 3D-HST survey. We find that
these PSBs are more compact than the general population of quiescent galaxies,
lying systematically $\mathrm{\sim\,0.1\,dex}$ below the established size-mass
relation. However, their central surface mass densities are similar to those of
their quiescent counterparts
($\mathrm{\,log(\Sigma_{1\,kpc}/(M_{\odot}/kpc^2))\sim\,10.1}$). These findings
are easily reconciled by later ex-situ growth via minor mergers or a slight
progenitor bias. These PSBs are round in projection ($b/a_{median}\sim0.8$),
suggesting that they are primarily spheroids, not disks, in 3D. We find no
correlation between time since quenching and light-weighted PSB sizes or
central densities. This disfavors apparent structural growth due to the fading
of centralized starbursts in this galaxy population. Instead, we posit that the
fast quenching of massive galaxies at this epoch occurs preferentially in
galaxies with pre-existing compact structures.
