The formation of globular clusters (GC), with their multiple stellar generations, is still an unsolved puzzle. Thus, interest is rising on the possibility to detect their precursors at high redshift, hence directly witnessing their formation. A simple set of assumptions are empirically justified and then used to predict how many such precursors formed between redshift 3 and 10 could actually be detected by the NIRCam instrument on board of JWST. It is shown that the near power-law shape of the rest-frame UV continuum of young globular cluster precursors (GCP) implies that both colours and luminosities in NIRCam long-wavelength passbands depend remarkably weakly on formation redshift. Thus, the predicted number counts depend only little on the actual formation redshifts in the mentioned range, with the exception of the bluest passbands for which counts can be strongly suppressed by intergalactic absorption along the line of sight. Instead, counts depend strongly on the actual mass of GCPs, in such a way that one NIRCam pointing should detect of the order of 10 GCPs to mag ∼ 30 if their mass distribution was the same of today GCs, or over 1,000 if their mass was 10 times higher. Therefore, GCP number counts will set fairly tight constraints on the initial mass of GCs. An encouraging agreement with the number density of candidate GCPs at z=6-8, revealed by the Hubble Frontier Fields (HFF) program, suggests that their initial mass could be at least 4 times higher than that of their local descendants if all were to end up as GCs.