The structure and growth of the solid electrolyte interphase (SEI) region between an electrolyte and an electrode is one of the most fundamental yet less well-understood phenomena in solid-state batteries. We present an atomistic simulation of the SEI growth for one of the currently promising solid electrolytes (Li6PS5Cl), based on ab initio-trained machine learning interatomic potentials, for over 30,000 atoms during 10 ns, well beyond the capabilities of conventional molecular dynamics. This unveils a two-step growth mechanism: a Li-argyrodite chemical reaction leading to the formation of an amorphous phase, followed by a kinetically slower crystallization of the reaction products into a 5Li2S·Li3P·LiCl solid solution. The simulation results support the recent, experimentally founded hypothesis of an indirect pathway of electrolyte reduction. These findings shed light on the intricate processes governing SEI evolution, providing a valuable foundation for the design and optimization of next-generation solid-state batteries.