High-intensity laser plasma-based ion accelerators provide unsurpassed field gradients in the megavolt-per-micrometer range. They represent promising candidates for next-generation applications such as ion beam cancer therapy in compact facilities. The weak scaling of maximum ion energies with the square-root of the laser intensity, established for large sub-picosecond class laser systems, motivates the search for more efficient acceleration processes. Here we demonstrate that for ultrashort (pulse duration ~30 fs) highly relativistic (intensity ~10(21) W cm(-2)) laser pulses, the intra-pulse phase of the proton acceleration process becomes relevant, yielding maximum energies of around 20 MeV. Prominent non-target-normal emission of energetic protons, reflecting an engineered asymmetry in the field distribution of promptly accelerated electrons, is used to identify this pre-thermal phase of the acceleration. The relevant timescale reveals the underlying physics leading to the near-linear intensity scaling observed for 100 TW class table-top laser systems.