I'm asking mainly from the video games CK2 and EU4. In CK2, the only way you can raise an army is by raising your levies and the like. In EU4, you ahve to build armies over time. The problem is, there is like 0 years between the two games. In real life, when did the change happen?
During antiquity, whenever a nation became too large for levies to be able to do a campaign and return home to farm, like what happened in Rome at the end of 2nd century B.C or when the nation became prosperous enough to be able to field standing armies. If I recall correctly, Philip II of Makedon formed a standing army. In the medieval period, the first standing armies were the Ottoman janissaries who were acquired from christian regions when they were children and were trained from youth to be soldiers. They were still supplemented with levies for atleast the whole medieval period. In Western Europe, the first model of standing armies were the Spanish tercios.
Also, in CK2, with the Byzantine DLC ("Legacy of Rome", was it?) you are able to form standing retinues, elite groups to be supplemented with (or to supplement) the levies. Retinues would be the predecessors to standing armies of the nation you'd have in EU4.