Depends on what options and technologies you have available, and how do you deploy your website.

There are CMSs which update existing static pages through FTP: You provide access credentials, mark editable parts of your HTML in a markup, and then edit the content through the hosted CMS. I know two systems which work like that: Cushy CMS and Surreal CMS.

If the source of your site is versioned through Git (and hosted on GitHub), you have other options, like Netlify CMS, Spinal CMS, Siteleaf, Forestry, or CloudCannon. Some of these also need you to use static site generator (like 11ty, Jekyll, or Hugo).

If you have some server-side scripting support available (typically PHP) you can also consider some flat-file based, server-side systems, like Kirby CMS or Lektor, which are usually simpler to retrofit into an existing template than “traditional” CMSs (WordPress, Drupal).

Finally, you could also use a desktop-based static site generator which provides a user-friendly GUI, and then locally generates and uploads the website. For example Publii, YouDoCMS, Agit CMS.

If you're looking for a simple to-integrate CMS, Contentful is a good option. Their free option is quite useful so you don't have to pay unless the website requires a lot of content, assets, etc. To connect to it you just need to make a request from the website and decide which content you want. I believe it uses graphql for getting the content.