We present the results of a study of the demographics of low-mass stellar systems at high redshift in a suite of cosmological simulations from the First Billion Years Project (FiBY). We have identified a population of objects at z=6 which we believe show characteristics to be early ancestors of local Universe globular clusters (GCs), which we dub “infant GC candidates”. These candidates are compact in size, have little dark matter and high gas content, thus they are likely to host further episodes of star formation. From their evolution until z=6, the process of star formation in these objects appears to be bursty in nature, which could be an early manifestation of the ‘multiple population phenomenon’ we currently observe in low-redshift GCs. In our simulations, these high-density GC ancestors tend to form in groups located within the disks of their host galaxies. We also propose a new link between present-day globulars and their high-redshift counterparts, which we have identified by studying the global properties of these infant GC candidates and the relationship with their large-scale environment. We find that the relation between the specific star formation rate of a host galaxy and the mass of the most massive GC holds across a large range of redshifts, thus providing a powerful way to probe both the early evolution of this class of stellar systems as well star formation across cosmic time.