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Biogas production estimation has been one of the most important and challenging objectives for anaerobic digestion processes due to the complexity of its dynamics and the lack of high-quality open-access datasets. This study presents a hybrid modeling framework that combines a mechanistic model, based on ordinary differential equations (ODE), with a machine learning model. Rather than relying exclusively on experimental data, the proposed approach leverages physics-informed synthetic data generation, complemented by a lag-based feature engineering to capture inherent temporal dependencies in the process dynamics available in operational data of a bio-digester. Two configurations were evaluated: a baseline model and an enhanced version incorporating lag features and simplified temperature profile. While the improved model achieved high predictive performance (R2=0.97885, RMSE=131.80[L/d]), additional analyses reveal that this performance is partly driven by temporal memory and remains sensitive to noise and feature composition. Instead of presenting the model as a final solution, this work frames it as a step toward practical digital twin implementations, acknowledging the gap that still exists between simulation-based accuracy and real-world reliability.