One of the attractive properties of Fiber Reinforced Polymer (FRP) composites is their damage tolerance, the ability to sustain loads above their initial strength. To fully exploit the potential of FRP composites, it is important to measure, understand and simulate the evolution of fracture. We present a method that incorporates efficient finite element continuum damage simulations, global sensitivity analyses, and data-driven regression approaches to rapidly estimate the mechanical behavior of FRP composites subjected to progressive fracture tests. We develop various data-driven surrogate models, including deterministic machine learning (ML) techniques such as linear regression and neural networks; as well as probabilistic ML methods such as Gaussian Process Regression. These models are based on the most influential finite element input parameters identified through advanced sensitivity analyses. The results of this study provide a foundation for efficient uncertainty quantification regarding the structural integrity of composites, where only rapid and efficient modeling approaches are feasible due to the need for many model evaluations and large datasets. Such rapid models with the ability to account for uncertainty have the potential to significantly reduce the cost and time associated with certifying aerospace composite structures, thus accelerating the development and implementation of next-generation high-performance FRP composites.