The growth of lithium dendrites in inorganic solid electrolytes is an essential drawback that hinders the development of reliable all-solid-state lithium metal batteries. Generally, ex situ post mortem measurements of battery components show the presence of lithium dendrites at the grain boundaries of the solid electrolyte. However, the role of grain boundaries in the nucleation and dendritic growth of metallic lithium is not yet fully understood. Here, to shed light on these crucial aspects, we report the use of operando Kelvin probe force microscopy measurements to map locally time-dependent electric potential changes in the Li_6.25Al_0.25La₃Zr₂O₁₂ garnet-type solid electrolyte. We find that the Galvani potential drops at grain boundaries near the lithium metal electrode during plating as a response to the preferential accumulation of electrons. Time-resolved electrostatic force microscopy measurements and quantitative analyses of lithium metal formed at the grain boundaries under electron beam irradiation support this finding. Based on these results, we propose a mechanistic model to explain the preferential growth of lithium dendrites at grain boundaries and their penetration in inorganic solid electrolytes.