Climate-driven flash floods increasingly threaten lives and infrastructure in data-scarce small catchments. This study proposes a hybrid framework integrating physically-based hydrodynamic modeling with a Long Short-Term Memory (LSTM) surrogate model to enable rapid and accurate forecasts. The framework innovatively generates physics-guided synthetic training data through high-fidelity hydrodynamic simulations, effectively circumventing reliance on scarce historical runoff records. The LSTM surrogate model, trained exclusively on computationally generated rainfall-runoff scenarios, achieves high accurate predictions comparable to hydrodynamic simulations (RMSE: 0.358-0.494 m3/s). Meanwhile, the surrogate model outperforming traditional methods by 2-3 orders of magnitude in computational efficiency, effectively overcoming the computational efficiency barrier. By bridging the accuracy-speed dichotomy through physics-informed machine learning, the proposed framework establishes a new paradigm for real-time flood risk management in observation-poor environments.