Over the last decade, the world has witnessed many breakthroughs in artificial intelligence, largely due to advances in deep learning technology. Notably, computer vision solutions have significantly contributed to these achievements. Human face analysis, a core area of computer vision, has gained considerable attention due to its wide applicability in fields such as law enforcement, social media, and marketing. However, existing methods for facial age estimation often struggle with accuracy due to limited feature extraction capabilities and inefficiencies in learning hierarchical representations. This paper introduces a novel framework to address these issues by proposing a Multi-Stage Deep Neural Network (MSDNN) architecture. The MSDNN architecture divides each CNN backbone into multiple stages, enabling more comprehensive feature extraction, thereby improving the accuracy of age predictions from facial images. Our framework demonstrates a significant performance improvement over traditional solutions, with its effectiveness validated through comparisons with the EfficientNet and MobileNetV3 architectures. The proposed MSDNN architecture achieves a notable decrease in Mean Absolute Error (MAE) across three widely used public datasets (MORPH2, CACD, and AFAD) while maintaining a virtually identical parameter count compared to the initial backbone architectures. These results underscore the effectiveness and feasibility of our methodology in advancing the field of age estimation, showcasing it as a robust solution for enhancing the accuracy of age prediction algorithms.