Multiple phenomena occurring at the microscopic scale affect the final mechanical performance of composite parts manufactured through processes involving impregnation of dry fibers, such as resin transfer molding. Formation of fiber-poor areas in specific locations or air entrapment within the resin are issues that commonly arise during the impregnation. Such challenges have motivated the use of numerical simulations to understand the manufacturing processes better and to optimize the process design. However, the limitation imposed by their computational cost has encouraged the use of machine learning (ML) to replace them. Thus far, the state of the art has focused on predicting the permeability of fiber-reinforced microstructures. We expand the limits by proposing an ML-based surrogate for microscale steady-state velocity prediction of a fluid flowing through a fibrous microstructure. This model, inspired by the U-net architecture, takes as input the image representation of fiber-reinforced composite microstructures. It subsequently outputs the resin velocity field around the fibers based on prescribed boundary conditions. Those results are further used to estimate the permeability of the microstructures, thus encompassing previous works. We describe in this work the computational pipeline of our approach, starting from generation of the ground truth data to the optimization of the UNet hyperparameters.@en