With the advent of JWST, we can probe the rest-frame optical emission of galaxies at $z\gt 3$ with high sensitivity and spatial resolution, making it possible to accurately characterize red, optically faint galaxies and thus move towards a more complete census of the galaxy population at high redshifts. To this end, we present a sample of 148 massive, dusty galaxies from the JWST/Cosmic Evolution Early Release Science survey, colour-selected using solely JWST bands. With deep JWST/NIRCam data from 1.15 to 4.44 $\mu$m and ancillary HST/ACS and WFC3 data, we determine the physical properties of our sample using spectral energy distribution fitting with bagpipes. We demonstrate that our selection method efficiently identifies massive ($\mathrm{\langle \log {\it M}_\star /M_\odot \rangle \sim 10}$) and dusty ($\mathrm{\langle {\it A}_V\rangle \sim 2.7\ mag}$) sources, with a majority at $z\,\gt\, 3$ and predominantly lying on the galaxy main sequence. The main results of this work are the stellar mass functions (SMFs) of red, optically faint galaxies from redshifts between $3\,\lt\, z\,\lt\, 8$: these galaxies make up a significant relative fraction of the pre-JWST total SMF at $3\,\lt\, z\,\lt\, 4$ and $4\,\lt\, z\,\lt\, 6$, and dominate the high-mass end of the pre-JWST SMF at $6\,\lt\, z\,\lt \,8$, suggesting that our census of the galaxy population needs amendment at these epochs. While larger areas need to be surveyed in the future, our results suggest already that the integrated stellar mass density at $\mathrm{\log {\it M}_\star /M_\odot \ge 9.25}$ may have been underestimated in pre-JWST studies by up to $\sim$15–20% at $z\sim 3{\!-\!}6$, and up to $\sim$45% at $z\sim 6{\!-\!}8$, indicating the rapid onset of obscured stellar mass assembly in the early Universe.