Erosion of metallic surfaces due to the permanent impact of high-speed water droplets is a significant concern in diverse industrial applications like turbine blades, among others. In the initial stage of water droplet erosion, there is an incubation regime with negligible mass loss whose duration is strongly dependent on water droplet sizes and velocities, the initial state of the surface, and the material properties of the target. The prediction of the incubation period duration is one of the main topics of research in the field. In this work, the interaction of the water droplets with a metallic surface is simulated using a hybrid Smoothed-Particle Hydrodynamics/Finite Element Method modeling scheme. The effect of multiple random impacts on representative target areas for certain ranges of impact angles and velocities was studied using a combination of simple material and damage models for the target surface of Ti-6Al-4V titanium alloy. The simulation is able to reproduce the main dependencies of the incubation regime and the first stages of water droplet erosion on the impact angle and velocity as reported in the literature. This framework can be considered a foundation for more advanced models with the goal of a better understanding of the physical mechanisms behind the incubation regime in order to devise strategies to extend it in real applications.