  We report the discovery of 15 exceptionally luminous $10\lesssim z\lesssim14$
candidate galaxies discovered in the first 0.28 deg$^2$ of JWST/NIRCam imaging
from the COSMOS-Web Survey. These sources span rest-frame UV magnitudes of
$-20.5>M_{\rm UV}>-22$, and thus constitute the most intrinsically luminous
$z\gtrsim10$ candidates identified by JWST to-date. Selected via NIRCam imaging
with Hubble ACS/F814W, deep ground-based observations corroborate their
detection and help significantly constrain their photometric redshifts. We
analyze their spectral energy distributions using multiple open-source codes
and evaluate the probability of low-redshift solutions; we conclude that 12/15
(80%) are likely genuine $z\gtrsim10$ sources and 3/15 (20%) likely
low-redshift contaminants. Three of our $z\sim12$ candidates push the limits of
early stellar mass assembly: they have estimated stellar masses
$\sim5\times10^{9}\,M_\odot$, implying an effective stellar baryon fraction of
$\epsilon_{\star}\sim0.2-0.5$, where $\epsilon_{\star}\equiv
M_{\star}/(f_{b}M_{halo})$. The assembly of such stellar reservoirs is made
possible due to rapid, burst-driven star formation on timescales $<$100\,Myr
where the star-formation rate may far outpace the growth of the underlying dark
matter halos. This is supported by the similar volume densities inferred for
$M_\star\sim10^{10}\,M_\odot$ galaxies relative to $M_\star\sim10^{9}\,M_\odot$
-- both about $10^{-6}$ Mpc$^{-3}$ -- implying they live in halos of comparable
mass. At such high redshifts, the duty cycle for starbursts would be of order
unity, which could cause the observed change in the shape of the UVLF from a
double powerlaw to Schechter at $z\approx8$. Spectroscopic redshift
confirmation and ensuing constraints of their masses will be critical to
understanding how, and if, such early massive galaxies push the limits of
galaxy formation in $\Lambda$CDM.
