  We present the discovery and analysis of SN\,2022oqm, a Type Ic supernova
(SN) detected $<1$\,day after explosion. The SN rises to a blue and short-lived
(2\,days) initial peak. Early-time spectral observations of SN\,2022oqm show a
hot (40,000\,K) continuum with high-ionization C and O absorption features at
velocities of 4000\,km\,s$^{-1}$, while its photospheric radius expands at
20,000\,\kms, indicating a pre-existing distribution of expanding C/O material.
After $\sim2.5$\,days, both the spectrum and light curves evolve into those of
a typical SN Ic, with line velocities of $\sim10,000$\,km\,s$^{-1}$, in
agreement with the photospheric radius evolution. The optical light curves
reach a second peak at $t\approx15$\,days. By $t=60$\,days, the spectrum of
\oqm\ becomes nearly nebular, displaying strong \ion{Ca}{2} and [\ion{Ca}{2}]
emission with no detectable [\ion{O}{1}], marking this event as Ca-rich. The
early behavior can be explained by $10^{-3}$\,\msun\ of optically thin
circumstellar material (CSM) surrounding either (1) a massive compact
progenitor such as a Wolf-Rayet star, (2) a massive stripped progenitor with an
extended envelope, or (3) a binary system with a white dwarf. We propose that
the early-time light curve is powered by both interaction of the ejecta with
the optically thin CSM and shock cooling (in the massive-star scenario). The
observations can be explained by CSM that is optically thick to X-ray photons,
is optically thick in the lines as seen in the spectra, and is optically thin
to visible-light continuum photons that come either from downscattered X-rays
or from the shock-heated ejecta. Calculations show that this scenario is
self-consistent.
