We present the discovery and analysis of SN 2022oqm, a Type Ic supernova (SN) detected <1 day after the 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 km s$^‑1$, indicating a pre-existing distribution of expanding C/O material. After ∼2.5 days, both the spectrum and light curves evolve into those of a typical SN Ic, with line velocities of ∼10,000 km s$^‑1$, in agreement with the evolution of the photospheric radius. The optical light curves reach a second peak at t ≈ 15 days. By t = 60 days, the spectrum of SN 2022oqm becomes nearly nebular, displaying strong Ca II and [Ca II] emission with no detectable [O I], marking this event as Ca-rich. The early behavior can be explained by 10$^‑3$ M $_ødot$ 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 the 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.