Neurodevelopmental disorders such as Fragile X Syndrome (FXS) and Autism Spectrum Disorder (ASD) are characterized by disrupted cortical oscillatory activity, particularly in the alpha and gamma frequency bands. These abnormalities are linked to deficits in attention, sensory processing, and cognitive function. In this work, we present an adaptive machine learning-based brain-computer interface (BCI) system designed to modulate neural oscillations through frequency-specific auditory stimulation to enhance cognitive readiness in individuals with FXS. EEG data were recorded from 38 participants using a 128-channel system under a stimulation paradigm consisting of a 30-second baseline (no stimulus) followed by 60-second auditory entrainment episodes at 7Hz, 9Hz, 11Hz, and 13Hz. A comprehensive analysis of power spectral features (Alpha, Gamma, Delta, Theta, Beta) and cross-frequency coupling metrics (Alpha-Gamma, Alpha-Beta, etc.) was conducted. The results identified Peak Alpha Power, Peak Gamma Power, and Alpha Power per second per channel as the most discriminative biomarkers. The 13Hz stimulation condition consistently elicited a significant increase in Alpha activity and suppression of Gamma activity, aligning with our optimization objective. A supervised machine learning framework was developed to predict EEG responses and dynamically adjust stimulation parameters, enabling real-time, subject-specific adaptation. This work establishes a novel EEG-driven optimization framework for cognitive neuromodulation, providing a foundational model for next-generation AI-integrated BCI systems aimed at personalized neurorehabilitation in FXS and related disorders.