A new simulation-statistical optimization strategy for optimum design of a multi-source renewable energy air conditioning system that includes an absorption chiller (AC), a desiccant wheel, photovoltaic/thermal (PV/T) panels, ground source heat exchanger (GSHE), and thermal energy storage unit filled with phase change materials (PCMs) is developed in this study. The strategy is created by combining the transient-based simulation and response surface method (TRN-RSM) to achieve the optimal energy, economic, and environmental (3E) design of the hybrid cooling and heating system with a realistic computational cost over the system’s 25-year lifespan. Desiccant wheel and AC subsystems are used to manage the latent and sensible load of the building separately. The interaction of main design parameters on the 3E indicators is also investigated. The annual electricity and natural gas consumption of the system using the optimum system identified by TRN-RSM decreased by 14.6% and 51.8%, respectively, when compared to the conventional system. The findings reveal considerable progress in all 3E objective functions compared to conventional systems. It was also found that the electricity generated by the optimal number of PV/T panels can change the system from a financially unprofitable investment to a profitable one.