The NOrthern Extended Millimeter Array (NOEMA) formIng Cluster survEy (NICE) is a NOEMA large programme targeting 69 massive galaxy group candidates at z > 2 over six deep fields with a total area of 46 deg2. Here we report the spectroscopic confirmation of eight massive galaxy groups at redshifts 1.65 ≤ z ≤ 3.61 in the Cosmic Evolution Survey (COSMOS) field. Homogeneously selected as significant overdensities of red IRAC sources that have red Herschel colours, four groups in this sample are confirmed by CO and [CI] line detections of multiple sources with NOEMA 3 mm observations, three are confirmed with Atacama Large Millimeter Array (ALMA) observations, and one is confirmed by Hα emission from Subaru/FMOS spectroscopy. Using rich ancillary data in the far-infrared and sub-millimetre, we constructed the integrated far-infrared spectral energy distributions for the eight groups, obtaining a total infrared star formation rate (SFR) of 260–1300 M⊙ yr‑1. We adopted six methods for estimating the dark matter masses of the eight groups, including stellar mass to halo mass relations, overdensity with galaxy bias, and NFW profile fitting to radial stellar mass densities. We find that the radial stellar mass densities of the eight groups are consistent with a NFW profile, supporting the idea that they are collapsed structures hosted by a single dark matter halo. The best halo mass estimates are log(Mh/M⊙) = 12.8 ‑ 13.7 with a general uncertainty of 0.3 dex. Based on the halo mass estimates, we derived baryonic accretion rates (BARs) of (1 ‑ 8)×103 M⊙/yr for this sample. Together with massive groups in the literature, we find a quasi-linear correlation between the integrated SFR/BAR ratio and the theoretical halo mass limit for cold streams, Mstream/Mh, with SFR/BAR = 10‑0.46 ± 0.22(Mstream/Mh)0.71 ± 0.16 with a scatter of 0.40 dex. Furthermore, we compared the halo masses and the stellar masses with simulations, and find that the halo masses of all structures are consistent with those of progenitors of Mh(z = 0) > 1014 M⊙ galaxy clusters, and that the most massive central galaxies have stellar masses consistent with those of the brightest cluster galaxy progenitors in the TNG300 simulation. Above all, the results strongly suggest that these massive structures are in the process of forming massive galaxy clusters via baryonic and dark matter accretion.