The cosmic near-infrared background (NIRB) offers a powerful integral probe of radiative processes at different cosmic epochs, including the pre-reionization era when metal-free, Population III (Pop III) stars first formed. In Sun et al. (2021b), we constructed a theoretical model for the cosmic NIRB signal contributed by the first stars. We find that in circumstances where massive Pop III stars persistently form in molecular cooling haloes, before being suppressed towards the epoch of reionization (EoR) by the accumulated Lyman-Werner background, a unique spectral signature shows up in the observed NIRB spectrum sourced by high-redshift galaxies. Such imprint will be in principle detectable by forthcoming space missions such as the Spectro-Photometer for the History of the Universe, Epoch of Reionization and Ices Explorer (SPHEREx). As a result, new constraints on the abundance and formation history of Pop III stars at high redshifts will be available through precise measurements of the NIRB in the next few years, which will also have important implications for other probes of the reionization like the global 21-cm signal.