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Investigating atom-surface interactions is the key to an in-depth understanding of chemical processes at interfaces, which are of central importance in many fields -- from heterogeneous catalysis to corrosion. In this work, we present a joint experimental and theoretical effort to gain insights into the atomistic details of hydrogen atom scattering at the $\alpha$-Al$_2$O$_3$(0001) surface. Surprisingly, this system has been hardly studied to date, although hydrogen atoms as well as $\alpha$-Al$_2$O$_3$ are omnipresent in catalysis as reactive species and support oxide, respectively. We address this system by performing hydrogen atom beam scattering experiments and molecular dynamics (MD) simulations based on a high-dimensional machine learning potential trained to density functional theory data. Using this combination of methods we are able to probe the properties of the multidimensional potential energy surface governing the scattering process. Specifically, we compare the angular distribution and the kinetic energy loss of the scattered atoms obtained in experiment with a large number of MD trajectories, which, moreover, allow to identify the underlying impact sites at the surface.