Quantum field theory predicts a nonlinear response of the vacuum to strong electromagnetic fields of macroscopic extent. This fundamental tenet has remained experimentally challenging and is yet to be tested in the laboratory. A particularly distinct signature of the resulting optical activity of the quantum vacuum is vacuum birefringence. This offers an excellent opportunity for a precision test of nonlinear quantum electrodynamics in an uncharted parameter regime. Recently, the operation of the high-intensity Relativistic Laser at the X-ray Free Electron Laser provided by the Helmholtz International Beamline for Extreme Fields has been inaugurated at the High Energy Density scientific instrument of the European X-ray Free Electron Laser. We make the case that this worldwide unique combination of an X-ray free-electron laser and an ultra-intense near-infrared laser together with recent advances in high-precision X-ray polarimetry, refinements of prospective discovery scenarios and progress in their accurate theoretical modelling have set the stage for performing an actual discovery experiment of quantum vacuum nonlinearity.