This is all on itself a sign that your project is fundamentally broken, but this is already covered by scenario b) incremental builds.
Even if for some reason you resist the urge of following best practices and not create your own problems, there are a myriad of techniques to limit the impact of touching a single file in your builds. Using a facade class to move your serialized JSON to an implementation detail of a class is perhaps the lowest effort one, but the textbook example would be something like a PIMPL.
The main problem with the build time of C++ projects are not the build times per se but clueless developers, who are oblivious to the problem domain, fumbling basic things and ending up creating their own problems. Once one of them stops to ask themself why is the project taking so much time to build, more often than not you find yourself a few commits away from dropping build times to a fraction of the cost. Even onboarding something like ccache requires no more than setting an environment variable.
