Accurate and reliable prediction of streamflow is essential for effective flood monitoring and management, reservoir operation, and management of water supply system. However, this is generally hindered by biases and uncertainties caused by nonlinear operations, model parameterization, and inaccuracies in meteorological forecasts. The conventional machine learning (ML) and deep learning (DL) models often result in higher error rates as well as lower predictive accuracies due to manual tuning. In order to overcome the aforementioned shortcomings, the current study utilizes an innovative, nature-inspired metaheuristic algorithm, which is referred to as the Orangutan Optimization Algorithm (OOA), for streamflow prediction. This approach aims to enhance the predictive accuracy of Artificial Neural Networks (ANN) and Long Short-Term Memory Networks (LSTM) models for streamflow prediction. The model development and simulation is demonstrated using the daily streamflow time series data of the Gorai Railway Bridge station of the Gorai River in Bangladesh. Several statistical model performance evaluation metrics including Normalized Root Mean Squared Error (NRMSE), Kling-Gupta Efficiency (KGE), Mean Absolute Error (MAE), and coefficient of determination (R) are used to assess the prediction performance of each model at both training and testing phases. It is evident from the results that the hybrid ML (OOA-ANN) and DL (OOA-LSTM) models generate better prediction than that of the standalone ANN and LSTM models. The results also demonstrate that the hybrid OOA-ANN model has outperformed all the developed models. Thus, the current study conclusively proves that the hybrid ML models with advanced optimization algorithm is viable for the enhanced prediction of streamflow.