Biochemical conversion of waste/wastewater is attracting more attention as a sustainable approach and a viable bioenergy source. Nevertheless, the complexity of substrates such as livestock manure (LSM) which contains high refractory materials, restricts the stability/effectiveness of anaerobic digestion (AD). Thus, incorporating functionalized-hydrochar into AD, would mitigate these issues and uphold the performance. To predict biogas production as a function of hydrochar dose and time via an advanced machine-learning approach, the current study investigates the inaugural application of Random Vector Functional Link (RVFL) in conjunction with the Snow Geese Algorithm (SGA). In the proposed model, the data is split into training and test sets, whereas during the process of determining the suitable parameters of RVFL using SGA, the training is used. The testing set is applied to assess the quality of the best solution obtained from SGA. The models' performance was evaluated using various metrics, including the coefficient of determination (R²), root mean square error (RMSE), mean absolute error (MAE), and coefficient of variation (COV). The RVFL model, optimized with SGA, was compared to results from the RVFL with Whale Optimization Algorithm (WOA), Sine-Cosine Algorithm (SCA), and Grey Wolf Optimization (GWO). RVFL based on SGA achieved the highest prediction accuracy, with an R² of 0.998, RMSE of 7.476, MAE of 5.280, and COV of 4.281, significantly outperforming the standalone RVFL and other hybrid models. This study highlights the potential of using an advanced hybrid RVFL model for enhancing biogas prediction, providing a promising tool when using multifunctional nanomaterials for LSM-AD complex-system.