Precipitation-related extreme events are rapidly growing due to climate change, emphasizing the need for accurate hazard projections. To effectively model the convective phenomena driving severe precipitation, high-resolution estimates are crucial. Existing methods struggle with either insufficient expressiveness in capturing complex convective dynamics, due to the low resolution, or excessive computational demands. In response, we propose an innovative deep learning framework that efficiently harnesses available data to yield precise results. This model, based on graph neural networks, utilises two grids with different resolution and two sets of edges to represent spatial relationships. Employing as input ERA5 reanalysis atmospheric variables on an approximately 25 km grid, the framework produces hourly precipitation estimates on a finer 3 km grid. Findings are promising in accurately capturing yearly precipitation distribution and estimating cumulative precipitation during extreme events. Notably, the model demonstrates effectiveness in spatial regions not included in the training, motivating further exploration of its transferability potential.