Many approaches for addressing Global Optimization problems typically rely on relaxations of nonlinear constraints over specific mathematical primitives. This is restricting in applications with constraints that are black-box, implicit or consist of more general primitives. Trying to address such limitations, Bertsimas and Ozturk (2022) proposed OCTHaGOn as a way of solving black-box global optimization problems by approximating the nonlinear constraints using hyperplane-based Decision-Trees and then using those trees to construct a unified MIO approximation of the original problem. We provide significant extensions to this approach, by (i) approximating the original problem using a much richer family of MIO-representable ML models besides Decision Trees, (ii) proposing adaptive sampling procedures for more accurate ML-based constraint approximations, (iii) utilizing robust optimization to account for the uncertainty of the sample-dependent training of the ML models and (iv) leveraging a family of relaxations to address the infeasibilities of the final MIO approximation. We show the improvements resulting from those enhancements through a wide range of Global Optimization benchmarks. We demonstrate the promise of the enhanced approach in finding globally optimal solutions, and compare it with well-established global optimizers such as BARON.