Bringing optical microscopy to the shortest possible length and time scales has been a long-sought goal, connecting nanoscopic elementary dynamics with the macroscopic functionalities of condensed matter. Super-resolution microscopy has circumvented the far-field diffraction limit by harnessing optical nonlinearities1. By exploiting linear interaction with tip-confined evanescent light fields2, near-field microscopy3,4 has reached even higher resolution, prompting a vibrant research field by exploring the nanocosm in motion5,6,7,8,9,10,11,12,13,14,15,16,17,18,19. Yet the finite radius of the nanometre-sized tip apex has prevented access to atomic resolution20. Here we leverage extreme atomic nonlinearities within tip-confined evanescent fields to push all-optical microscopy to picometric spatial and femtosecond temporal resolution. On these scales, we discover an unprecedented and efficient non-classical near-field response, in phase with the vector potential of light and strictly confined to atomic dimensions. This ultrafast signal is characterized by an optical phase delay of approximately π/2 and facilitates direct monitoring of tunnelling dynamics. We showcase the power of our optical concept by imaging nanometre-sized defects hidden to atomic force microscopy and by subcycle sampling of current transients on a semiconducting van der Waals material. Our results facilitate access to quantum light–matter interaction and electronic dynamics at ultimately short spatio-temporal scales in both conductive and insulating quantum materials.