Alzheimer's disease (AD) remains a formidable challenge in modern healthcare, necessitating innovative approaches for its early detection and intervention. This study aimed to enhance the identification of individuals with mild cognitive impairment (MCI) at risk of developing AD. Leveraging advances in computational power and the extensive availability of healthcare data, we explored the potential of deep learning models for early prediction using medical claims data. We employed a bidirectional gated recurrent unit (BiGRU) deep learning model for predictive modeling of MCI progression across various prediction intervals, extending up to five years post-initial MCI diagnosis. The performance of the BiGRU model was rigorously compared with several machine-learning model baselines to evaluate its efficacy. Using a robust cross-validation methodology, the BiGRU emerged as the top-performing model, achieving an Area Under the Receiver Operating Characteristic Curve (AUC-ROC) of 0.833 (95% CI: 0.822, 0.843), an Area Under the Precision-Recall Curve (AUC-PR) of 0.856 (95% CI: 0.845, 0.867), and an F1-Score of 0.71 (95% CI: 0.694, 0.724) for a five-year prediction interval. The results indicate that BiGRU, utilizing longitudinal claims data, reliably predicts MCI-to-AD progression over a lengthy interval following the initial MCI diagnosis, offering clinicians a valuable tool for targeted risk identification and stratification.