Alzheimer's disease, as one of the major and progressive challenges in public health, requires innovative solutions for early and accurate diagnosis. This research presents a hybrid deep learning model for the early detection of Alzheimer's using MRI images. Unlike conventional approaches that rely solely on pre-trained models, the proposed model combines the VGG16 architecture with an auxiliary CNN path that includes Dense layers and dropout. This auxiliary path, as a key branch, plays a significant role in enhancing the extraction of complex features and reducing the risk of overfitting. To address the severe class imbalance in the MRI dataset (such as only 64 samples in the moderate symptom class), a combination of the complementary SMOTE and data augmentation methods was used, which together improved the model's generalization in classifying rare classes. The dataset used was extracted from the public Kaggle datasets. Furthermore, precise experimental analyses were conducted on key parameters such as learning rate, image dimensions, batch size, dropout rate, and optimizer type, leading to the selection of the optimal model configuration. The final model achieved an accuracy and F1-score of 99.5%, demonstrating excellent performance in diagnosing Alzheimer's patients. The results of this research indicate that the intelligent use of advanced deep learning architectures, combined with data engineering solutions, can effectively contribute to the development of intelligent medical diagnostic systems and more precise management of neurological diseases.