The application of Artificial Intelligence (AI) to structural and aerospace engineering is still emerging, with open questions regarding its suitability and best practices for real-world deployment. Composites enable lighter, sophisticated structures, but their complex failure behavior poses significant design challenges. While the literature shows that machine-learning models can be made to achieve a measure of accuracy as full surrogates to traditional methods, this work investigates a machine-learning-assisted workflow for the calibration of impact damage models for composite materials, with the aim of accelerating the structural design process, preserving FEM as the final arbitrator, and clarifying how AI-based surrogates can be reliably developed, interpreted, and deployed in engineering practice. The study focuses on the calibration of the widely used LS-DYNA material model MAT-054 for ballistic impact analyses. Accurate calibration of this model is essential for the design and certification of aerospace composite structures, yet remains difficult due to the non-physical nature and strongly coupled, non-linear interactions among the damage evolution parameters that govern stiffness degradation and element deletion. A surrogate model based on a Multi-Layer Perceptron (MLP) was trained on explicit finite element simulations of ballistic impact to map selected MAT-054 parameters to projectile residual velocity, a key design variable for impact resistance. Embedding this surrogate in a gradient-based inverse optimization framework transforms a largely manual, trial-and-error calibration procedure into a systematic and accelerated optimization task, with the potential to reduce calibration time by orders of magnitude when compared to the traditional workflow. The final MLP surrogate achieved high predictive accuracy on unseen test data. This research demonstrates a practical framework for integrating AI-based finite element surrogates into real-world engineering. It clarifies parameter selection, describes network architecture tuning strategies, and provides quantitative insights into how damage-evolution parameters influence resulting residual velocity and impact resistance.