The culmination of the glaciers in the European Alps during the Last Glacial Maximum (LGM) is one of the most intensively studied paleoglaciological events, but its trigger and forcing remain incompletely understood. Here, we provide evidence that the timing of this glacier maximum coincided within age uncertainties with a 3100 yr-long interval of subsurface warming (26.6 to 23.5 ka BP) as recorded by an archive preserved in caves, cryogenic carbonates. This interval of sustained permafrost degradation during one of the coldest intervals of the last glacial period calls for a fundamental change in the dry Arctic-style precipitation regime. Instead, heavy snowfall during autumn and early winter led to the accumulation of a seasonal snowpack insulating the ground from the winter chill. Combined with thermal modelling, the data provide compelling evidence that the LGM glacier advance in the Alps was fueled by intensive snowfall late in the year, likely sourced from the Mediterranean Sea.