Accurate sleep stage classification is essential for understanding sleep disorders and improving overall health. This study proposes a novel three-stage approach for sleep stage classification using ECG signals, offering a more accessible alternative to traditional methods that often rely on complex modalities like EEG. In Stages 1 and 2, we initialize the weights of two networks, which are then integrated in Stage 3 for comprehensive classification. In the first phase, we estimate key features using Feature Imitating Networks (FINs) to achieve higher accuracy and faster convergence. The second phase focuses on identifying the N1 sleep stage through the time-frequency representation of ECG signals. Finally, the third phase integrates models from the previous stages and employs a Kolmogorov-Arnold Network (KAN) to classify five distinct sleep stages. Additionally, data augmentation techniques, particularly SMOTE, are used in enhancing classification capabilities for underrepresented stages like N1. Our results demonstrate significant improvements in the classification performance, with an overall accuracy of 80.79% an overall kappa of 0.73. The model achieves specific accuracies of 86.70% for Wake, 60.36% for N1, 83.89% for N2, 84.85% for N3, and 87.16% for REM. This study emphasizes the importance of weight initialization and data augmentation in optimizing sleep stage classification with ECG signals.