Accurate waste classification is vital for achieving sustainable waste management and reducing the environmental footprint of urbanization. Misclassification of recyclable materials contributes to landfill accumulation, inefficient recycling, and increased greenhouse gas emissions. To address these issues, this study introduces HybridSOMSpikeNet, a hybrid deep learning framework that integrates convolutional feature extraction, differentiable self-organization, and spiking-inspired temporal processing to enable intelligent and energy-efficient waste classification. The proposed model employs a pre-trained ResNet-152 backbone to extract deep spatial representations, followed by a Differentiable Soft Self-Organizing Map (Soft-SOM) that enhances topological clustering and interpretability. A spiking neural head accumulates temporal activations over discrete time steps, improving robustness and generalization. Trained on a ten-class waste dataset, HybridSOMSpikeNet achieved a test accuracy of 97.39%, outperforming several state-of-the-art architectures while maintaining a lightweight computational profile suitable for real-world deployment. Beyond its technical innovations, the framework provides tangible environmental benefits. By enabling precise and automated waste segregation, it supports higher recycling efficiency, reduces contamination in recyclable streams, and minimizes the ecological and operational costs of waste processing. The approach aligns with global sustainability priorities, particularly the United Nations Sustainable Development Goals (SDG 11 and SDG 12), by contributing to cleaner cities, circular economy initiatives, and intelligent environmental management systems.