The U.S. Air Force seeks to improve lifecycle management of composite structures. Nondestructive characterization of damage is a key input to this framework. One approach to characterization is model-based inversion of ultrasound inspection data; however, the computational expense of simulating the response from damage represents a major hurdle for practicality. A surrogate forward model with greater computational efficiency and sufficient accuracy is, therefore, critical to enable damage characterization via model-based inversion. In this work, a surrogate model based on Gaussian process regression (GPR) is developed on the chirplet decomposition of the simulated quasi-shear scatter from delamination-like features that form a shadowed region within a representative composite layup. The surrogate model is called in the solution of the inverse problem for the position of the hidden delamination, which is achieved with <0.5% error in <20 min on a workstation computer for two unique test cases. These results demonstrate that solving the inverse problem from the ultrasonic response is tractable for composite impact damage with hidden delaminations.