Freshwater is the most precious resource for sustaining life, socio-economic development, and ensuring ecological health. The global water demand has surged nearly sixfold over the past century, presenting significant challenges in managing water resources, particularly in developing nations and mountainous regions. The river basins in the Indian Himalayas have a unique climate and geography that make them highly susceptible to flood and landslide events, especially during the monsoon season. Therefore, accurate and timely streamflow forecasting is crucial for mitigating disaster risks, managing water resources, and setting up effective early warning systems. The SWAT model is frequently utilized for simulating streamflow; however, their application may be constrained in data-scarce, mountainous regions. Recent advancements in machine learning algorithms offer innovative possibilities as they can identify intricate, nonlinear relationships within hydrological data. This study compared the performance of the SWAT model with that of XGBoost, Random Forest, and Long Short-Term Memory (LSTM) networks for streamflow simulation in the Bhagirathi River Basin. The goodness-of-fit statistics for the SWAT model showed good performance during both calibration (NSE = 0.79, RMSE = 61.95 m3/s, PBIAS = 0.96%) and validation phases (NSE = 0.74, RMSE = 79.75 m3/s, PBIAS = −5.58%) at the daily time scale. The Random Forest model outperformed the other machine learning models in validation, achieving an NSE value of 0.872 and the lowest RMSE value of 55.8 m3/s. The results of this study underscore the potential for incorporating data-driven machine learning models into operational hydrological forecasting systems, particularly in data-deficient, flood-prone areas, and adaptive water management in mountainous basins susceptible to risks.