Societies become breakthrough powerful under fairly specific historical conditions.
Competition in a concentrated area.
This covers most breakthrough shifts. Let’s give some examples.
Europe
A large number of kingdoms and republics, in constant competition. If you didn’t advance militarily, culturally (administration and culture matter) and technologically, you were in trouble. As administration improved and military technology changed to favor “despotic kings” like Louis XIV and Henry the VIIth (a very underrated King), decentralized and smaller power, internal (nobles) and external were brought under control. Constant warfare and other forms of competition lead to rapid advancement.