In this work, we present an experimental analysis and a numerical optimization study for the material parameter identification of an impact attenuator made of a brand new All-PP thermoplastic composite material subjected to an axial impact load. After an experimental characterization of the material, a Finite Element (FE) numerical model of the impact attenuator is created and simulated using the LS-DYNA explicit software. Subsequently, in order to capture the force-displacement trend of the crush experimental test, a fine-tuning of some relevant material parameters through surrogate-based optimization techniques is performed. The optimization process mainly consists of (1) defining a set of target points on the load-displacement curve where to evaluate the Mean Squared Error (MSE) between the numerical and the experimental values; (2) using a Design of Experiments technique to provide a sample set on which expensive deterministic simulations are performed; (3) constructing as many surrogate approximations as the number of target points in order to predict how the load values change over the parameters’ domain; (4) predicting an overall MSE surface that is optimized by means of a genetic algorithm in a sequential domain reduction iterative procedure. Results show a good agreement between the numerical and the experimental impact load and energy curves, and hence confirm that surrogate-based optimization is a valuable technique to refine the material parameters in the numerical simulation of composite structures.