This work presents a computationally efficient approach for extracting compact model parameters with minimal training requirements. Bayesian optimization (BO) is employed in multiple stages to predict the optimum compact model parameters. Through sequential processing, adaptive sampling, successive domain reduction, and fine-tuned objective functions, the framework achieves precise and efficient fitting of both global and local model parameters across a range of devices, all in a reduced number of iterations, irrespective of the compact model used.