The word purgatorium, used as a noun naming a place rather than an adjective describing a fire, is not older than the twelfth century. The historian Jacques Le Goff traced this in La Naissance du Purgatoire, 1981, translated as The Birth of Purgatory, 1984, arguing that Purgatory as a third place, distinct from both Heaven and Hell rather than a stage folded inside either, crystallized only in the decades between roughly 1170 and 1215, bounded by Peter Comestor's early use of the noun and the Fourth Lateran Council. Before that window, patristic and early medieval writers described souls passing through a purifying fire, a process, not a location with its own geography.
Le Goff connected the shift to changes running through the same decades: the rise of scholastic theology at Paris, which pressed writers to define categories precisely rather than leave the afterlife in poetic suggestion; the Fourth Lateran Council's requirement of annual confession, which needed a coherent account of unfinished penance after death; and popular narratives that gave the new place entrances on earth, Saint Patrick's Purgatory, a cave on an island in Lough Derg where living pilgrims claimed to enter the afterlife directly, and the volcanoes of Sicily, read by medieval writers as chimneys venting Purgatory's fire into the visible world.
Le Goff's thesis has been contested on points of dating, and by scholars who find purgatorial ideas already implicit earlier, but the underlying observation, that a place needs a moment when it becomes a place, reframes Dante's mountain a century later. It is not an invention from nothing so much as the most complete answer yet given to a spatial question theology had only recently learned to ask.