Rapid floods induced by extreme precipitation are common events in regions near the Andes mountain range. Growing urban development, combined with the changing climate and the influence of El Niño, have increased the exposure of the population in many regions of South America. Simulations of flash floods in these watersheds are very challenging, due to the complex morphology, the insufficient hydrometeorological data, and the uncertainty posed by the variability of sediment concentration. To address these issues, we develop a high-resolution numerical model of the non-linear shallow water equations, coupled with the mass conservation of sediment, and considering the density effects and changes of rheology in the momentum equation. Based on these simulations we develop a real-time early-warning system, by creating a surrogate model or meta-model from the simulations. Using a small set of parameters, we define storms for a wide range of meteorological conditions, and utilize the high-fidelity model results to create a database of flood propagation under different conditions. Through this second model we perform a sophisticated interpolation/regression, and approximate efficiently the flow depths and velocities. This is the first application of its kind in the Andes region, which can be used to improve the prediction of flood hazard in real conditions, employing low computational resources. We also create a framework to develop early warning systems, and to help decision makers and city planners in these mountain regions.