In the medieval period, as soon as a cathedral (or church for that matter) was consecrated, it could have masses. We don't have consecration history of every cathedral in Europe, but based on those we do have, it seems that once a significant part of the nave, central apse and the ambulatory were built it would be consecrated - effectively when there was some cover from elements. That said, when Urban II was on tour of France preaching, among other things, what we know as the first crusade in 1090's, he consecrated many churches some of which barely had a central apse/altar. Note that consecration was not a function of Popes per se, but could be by bishop or arch bishop.

There are a number of partially built cathedrals still standing which were consecrated and held masses. I'm thinking of the Cathédrale Saint-Just-et-Saint-Pasteur de Narbonne which is immense but unfinished, yet still held mass in the apse/half nave with ambulatory from the late 13th century.