How to check which API's are available on a given machine?
Basic Vulkan availability can be checked by the presence of the loader dynamic library. This will reside in a standard place where you can load it with dlopen or LoadLibrary. 

If it fails to load then vulkan is not installed. If it does load then you can get the vkGetInstanceProcAddr function pointer from it with dlsymor GetProcAddress. After that you can query the devices as normal and decide whether or not it's sufficient to support your app.