We report a galaxy group candidate HPC1001 at Z ≈ 3.7 in the COSMOS field. This structure was selected as a high galaxy overdensity at Z > 3 in the COSMOS2020 catalog. It contains ten candidate members, of which eight are assembled in a 10′ × 10′ area with the highest sky density among known protoclusters and groups at Z > 3. Four out of ten sources were also detected at 1.2 mm with Atacama Large Millimeter Array continuum observations. Photometric redshifts, measured by four independent methods, fall within a narrow range of 3.5 < Z < 3.9 and with a weighted average of Z = 3.65 ± 0.07. The integrated far-IR-to-radio spectral energy distribution yields a total UV and IR star formation rate SFR ≈ 900 M·' yr-1. We also estimated a halo mass of ∼1013 M·' for the structure, which at this redshift is consistent with potential cold gas inflow. Remarkably, the most massive member has a specific star formation rate and dust to stellar mass ratio of Mdust/M∗ that are both significantly lower than that of star-forming galaxies at this redshift, suggesting that HPC1001 could be a Z ≈ 3.7 galaxy group in maturing phase. If confirmed, this would be the earliest structure in maturing phase to date, and an ideal laboratory to study the formation of the earliest quiescent galaxies as well as cold gas accretion in dense environments.