The dynamics of transient current distributions in superconducting YBa2Cu3O7−δ thin films were investigated during and immediately following an external field ramp, using high-speed (real-time) Magneto-Optical Imaging and calculation of dynamic current profiles. A number of qualitatively unique and previously unobserved features are seen in this novel analysis of the evolution of supercurrent during penetration. As magnetic field ramps up from zero, the dynamic current profile is characterized by strong peaks, the magnitude of which exceed the conventional critical current density (as determined from static current profiles). These peaks develop close to the sample edges, initially resembling screening currents but quickly growing in intensity as the external field increases. A discontinuity in field and current behaviour is newly observed, indicating a novel transition from increasing peak current toward relaxation behaviour. After this transition, the current peaks move toward the centre of the sample while reducing in intensity as magnetic vortices penetrate inward. This motion slows exponentially with time, with the current distribution in the long-time limit reducing to the expected Kim-model profile.