There are CMSes that work with static site generators. Static site generators do not imply that the input is markdown, though this is often the usecase. Any CMS that is decoupled from presentation, in fact, could be used for static site generation. Just read the structure and generate an appropriate HTML tree statically. Here are some CMSes with specific thought given to this use:
https://decapcms.org/
https://getkirby.com/
https://tina.io/
https://statamic.com/
ect ect