The 'Advanced Proton Driven Plasma Wakefield Acceleration Experiment' (AWAKE) aims to accelerate leptons via proton-beam-driven wakefield acceleration. It comprises extensive numerical studies as well as experiments at the CERN laboratory. The baseline scenario incorporates a plasma volume of approximately 62 cm3. The plasma wavelength is about 1.25 mm and needs to be adequately resolved, using a minimum of 130 points per plasma wavelength, in order to accurately reproduce the physics. The baseline scenario incorporates the proton beam micro-bunching, the concurrent nonlinear wakefield growth as well as the off-axis electron beam injection, trapping and acceleration. We present results for the first three-dimensional simulation of this baseline scenario with a full model, using a sufficient resolution. The simulation consumed about 22 Mch of computer resources and scaled up to 32 768 cores, thanks to a multitude of adaptions, improvements and optimization of the simulation code PSC. Through this large-scale simulation effort we were able to verify the results of reduced-model simulations as well as identify important novel effects during the electron injection process.