Background: Cognitive resilience is a critical factor in high-performance environments such as military operations, where sustained stress can impair attention and decision-making. In the present study, we utilized EEG and machine learning to assess cognitive resilience in elite military personnel. Methods: For this purpose, EEG signals were recorded from elite military personnel during stress-inducing attention-related and emotional tasks. The EEG signals were segmented into two temporal windows corresponding to the initial stress response (baseline) and the adaptive/recovery phase, extracting power spectral density features across delta, theta, alpha, beta, and gamma bands. Different machine learning models (Decision Tree, Random Forest, AdaBoost, XGBoost) were trained to classify temporal phases. Results: XGBoost achieved the highest accuracy (0.95), while Shapley Additive Explanations (SHAP) analysis identified delta and alpha bands (particularly in frontal and parietal regions) as key features associated with adaptive mental states. Conclusions: Our findings indicate that resilience-related neural responses can be successfully distinguished and that interpretable AI frameworks can be used for monitoring cognitive adaptation in high-stress environments.