We present a study of the investigation into the sensitivity of the strong coupling $\alpha_S(M^2_Z)$ using existing Deep Inelastic Scattering data from HERA and anticipated future measurements from the Electron Ion Collider (EIC) in a next-to-next-to-leading order QCD analysis. By combining simulated inclusive neutral current EIC data with HERA measurements, including charged and neutral current data, and optionally adding HERA inclusive jet and dijet data, the study aims to achieve a potentially world-leading level of precision. The results, obtainable with less than a year of projected EIC data at the lower end of the energy range, raise questions about uncertainties related to missing higher orders in the theoretical framework.