The solid electrolyte interphase in rechargeable Li-ion batteries, its dynamics and, significantly, its nanoscale structure and composition, hold clues to high-performing and safe energy storage. Unfortunately, knowledge of solid electrolyte interphase formation is limited due to the lack of in situ nano-characterization tools for probing solid-liquid interfaces. Here, we link electrochemical atomic force microscopy, three-dimensional nano-rheology microscopy and surface force-distance spectroscopy, to study, in situ and operando, the dynamic formation of the solid electrolyte interphase starting from a few 0.1 nm thick electrical double layer to the full three-dimensional nanostructured solid electrolyte interphase on the typical graphite basal and edge planes in a Li-ion battery negative electrode. By probing the arrangement of solvent molecules and ions within the electric double layer and quantifying the three-dimensional mechanical property distribution of organic and inorganic components in the as-formed solid electrolyte interphase layer, we reveal the nanoarchitecture factors and atomistic picture of initial solid electrolyte interphase formation on graphite-based negative electrodes in strongly and weakly solvating electrolytes.