We conduct a systematic search for protocluster candidates at $z \geq 6$ in the COSMOS field using the recently released COSMOS2020 source catalog. We select galaxies using a number of selection criteria to obtain a sample of galaxies that have a high probability of being inside a given redshift bin. We then apply overdensity analysis to the bins using two density estimators, a Weighted Adaptive Kernel Estimator and a Weighted Voronoi Tessellation Estimator. We have found 15 significant ($>4\sigma$) candidate galaxy overdensities across the redshift range $6\le z\le7.7$. The majority of the galaxies appear to be on the galaxy main sequence at their respective epochs. We use multiple stellar-mass-to-halo-mass conversion methods to obtain a range of dark matter halo mass estimates for the overdensities in the range of $\sim10^{11-13}\,M_{\rm \odot}$, at the respective redshifts of the overdensities. The number and the masses of the halos associated with our protocluster candidates are consistent with what is expected from the area of a COSMOS-like survey in a standard $\Lambda$CDM cosmology. Through comparison with simulation, we expect that all the overdensities at $z\simeq6$ will evolve into a Virgo-/Coma-like clusters at present (i.e., with masses $\sim 10^{14}-10^{15}\,M_{\rm \odot}$). Compared to other overdensities identified at $z \geq 6$ via narrow-band selection techniques, the overdensities presented appear to have $\sim10\times$ higher stellar masses and star-formation rates. We compare the evolution in the total star-formation rate and stellar mass content of the protocluster candidates across the redshift range $6\le z\le7.7$ and find agreement with the total average star-formation rate from simulations.