Designing Low Earth Orbit (LEO) constellations for the continuous, collaborative observation of space objects in MEO/GEO is a complex optimization task, frequently limited by prohibitive computational costs. This study introduces an efficient surrogate-based framework to overcome this challenge. Our approach integrates Optimized Latin Hypercube Sampling (OLHS) with a Radial Basis Function (RBF) model to minimize the required number of satellites. In a comprehensive case study targeting 18 diverse space objects—including communication satellites in GEO (e.g., EUTELSAT, ANIK) and navigation satellites in MEO/IGSO from GPS, Galileo, and BeiDou constellations—the method proved highly effective and scalable. It successfully designed a 208-satellite Walker constellation that provides 100% continuous coverage over a 36-h period. Furthermore, the design ensures that each target is simultaneously observed by at least three satellites at all times. A key finding is the method’s remarkable efficiency and scalability: the optimal solution for this larger problem was found using only 46 high-fidelity function evaluations, maintaining a computational time that was 5–8 times faster than traditional global optimization algorithms. This research demonstrates that surrogate-assisted optimization can drastically lower the computational barrier in constellation design, offering a powerful tool for building cost-effective and robust Space Situational Awareness (SSA) systems.