Metals (anything heavier than Helium) are made by stars, but when and where those stars existed in the Universe is an outstanding problem. X-ray observations show that the hot, X-ray emitting gas surrounding galaxy clusters, the intracluster medium (ICM), has a nearly universal metallicity of ZICM ≈ 0.4Z⊙. This metallicity is largely independent of stellar fraction, M∗/Mgas, and exceeds what is expected from present-day stellar populations under standard initial mass functions (IMFs). This discrepancy is known as the missing metal conundrum. Many theories have been posed to explain this mismatch, but fault has been found to each when compared with observations. The primary remaining theory yet to be disproved is the existence of an Early Enrichment Population (EEP) - a predominantly high-mass stellar population at z ∼ 10 − 6 that enriched the ICM while leaving a minimal surviving population. In this dissertation, I develop and test a quantitative framework for the EEP by combining detailed X-ray measurements, chemical evolution models, and constraints from supernovae and galaxy luminosity functions. I do this through a homogeneous study of 26 galaxy groups and clusters using archival XMM-Newton data, measuring radial metallicity profiles and the deriving the relation between ZICM and M∗/Mgas. With this I show that an additional metal component, ZEEP is required even when updated yields, remnants, and non closed-box behavior in groups are taken into account when deriving the contribution from the visible stellar populations, Z∗. I then construct theoretical models for the EEP, exploring a range of IMFs and using Type Ia supernovae (SNe Ia) rates to identify IMFs that reproduce both the required metal yield and present-day observables. I further constrain the low-mass end of the EEP IMF by requiring that the residual light from long-lived EEP stars not exceed the observed luminosity of dwarf elliptical galaxies that dominate the low-luminosity component of cluster luminosity functions. Together, these results provide the first observationally anchored, testable constraints on the EEP and its IMF, and establish concrete predictions for high-redshift supernovae and dwarf galaxy light that can be probed with current and future telescopes such as the James Webb Space Telescope.