25 thousand years ago, the European Alps were covered by a kilometre-thick body of ice, commonly described as the Alpine Ice Field. Numerical modelling of this glaciation has been challenged by persistent model-data disagreements, including large overestimations of its former thickness. Here, we tackle this issue by applying the Instructed Glacier Model, a three-dimensional, high-order, and thermo-mechanically coupled model enhanced with physics-informed machine learning. This new approach allows us to produce an ensemble of 100, Alps-wide and 17 thousand-year-long (35-18 ka) simulations at 300 m spatial resolution. Unfeasible with traditional models due to computational costs, our experiment substantially increases model-data agreement in both ice extent and thickness. The model-data offset in ice thickness, for instance, is here reduced by between 200% and 450% relative to previous studies. The results yield implications for more accurately reconstructing former ice velocities, ice temperature, basal conditions, glacial erosion processes, glacial isostatic adjustment, and climate evolution in the Alps during the last glaciation. Furthermore, this study demonstrates that physics-informed AI-driven glacier evolution models can overcome the bottleneck of high-resolution continental-scale modelling required to accurately describe complex topographies and ice dynamics.