Tailored nanostructures can confine electromagnetic waveforms in extremely sub-wavelength volumes, opening new avenues in lightwave sensing and control down to sub-molecular resolution. Atomic light-matter interaction depends critically on the absolute strength and the precise time evolution of the near field, which may be strongly influenced by quantum-mechanical effects. However, measuring atom-scale field transients has remained out of reach. Here we introduce quantitative atomic-scale waveform sampling in lightwave scanning tunnelling microscopy to resolve a tip-confined near-field transient. Our parameter-free calibration employs a single-molecule switch as an atomic-scale voltage standard. Although salient features of the far-to-near-field transfer follow classical electrodynamics, we develop a comprehensive understanding of the atomic-scale waveforms with time-dependent density functional theory. The simulations validate our calibration and confirm that single-electron tunnelling ensures minimal back-action of the measurement process on the electromagnetic fields. Our observations access an uncharted domain of nano-opto-electronics where local quantum dynamics determine femtosecond atomic near fields.