Accurate demand forecasting is a cornerstone of supply chain and logistics management, yet traditional statistical approaches—such as moving averages, exponential smoothing, and ARIMA—struggle to capture the nonlinearities and volatility of modern business environments. Although deep learning methods have demonstrated superior predictive performance, their reliance on large, high-quality datasets limits their applicability in contexts marked by data scarcity and uncertainty. This study addresses this gap by proposing a novel hybrid forecasting model that integrates Grey System Theory, specifically the GM (1,1) model, with Deep Neural Networks (DNNs). The GM (1,1) component provides robust estimations under minimal data conditions, while the DNN refines residual structures to model complex nonlinear dependencies. Empirical validation using container demand (TEU’s) data from Ensenada Port (2015–2024) demonstrates that the hybrid model outperforms standalone GM (1,1) in terms of MAPE, MPE, and RMSE, offering enhanced accuracy with minimal computational complexity. The results highlight the methodological contributions of combining interpretability and transparency from grey models with the adaptive learning capacity of neural networks. Beyond logistics, this framework is transferable to other data-constrained domains, such as public health surveillance, environmental monitoring, and economic forecasting. Overall, the proposed approach contributes to the advancement of intelligent forecasting systems capable of supporting decision-making under uncertainty, with practical value for both academia and industry.