Metal-poor globular clusters (MPGCs) are a unique probe of the early universe, in particular the reionization era. A popular hypothesis is that the observed truncation of MPGC formation is due to reionization. Under this hypothesis, constraining the formation epoch of MPGCs provides a complementary constraint on the epoch of reionization. Moreover, as the earliest reionizing sources first formed in galaxy clusters, systems of globular clusters in galaxy clusters are of particular interest. We provide a self-consistent dark matter only zoom cosmological simulation to perform an analysis of the Virgo cluster globular cluster system by identifying the present-day globular cluster system with early, rare dark matter peaks. By analysing both the line-of-sight velocity dispersion and the surface density profile of the present-day distribution, we are able to constrain the redshift and mass of the dark matter peaks. Although found to be degenerate, we quantify a dependence on the chosen line of sight of these quantities, whose strength varies with redshift. Coupled with star formation efficiency arguments, we find a best-fitting formation mass and redshift of ≃5 × 108 M⊙ and z ≃ 9. We predict ≃300 intracluster MPGCs in the Virgo cluster. Our results confirm the techniques pioneered by Moore et al. when applied to the Virgo cluster and extend and justify the analytic results of Spitler et al. numerically.