You typically hook up changes in your data with static site rebuilds.
Thinking of it as a cache has some merit, but it is more exciting to think of it as a event driven system as a whole, where instead of triggering a render on demand (user wants to look at something) you trigger it when a change happens.
This pattern reduces the need for ad hoc caching and eliminates some accidental complexity as well because it reduces the coupling of management and representation.