Been doing that for some small sites with Google Sheets, Jekyll and Netlify (https://www.netlify.com).

Wrote this plugin for Jekyll that'll let you use a Sheet as a data-source when building the site:

https://github.com/netlify/jekyll-gdrive

Netlify can run Jekyll builds with custom plugins (unlike GitHub pages) and you can setup an inbound webhook to trigger a build.

Once the webhook for building the site is in place, you can add a script like this to the Google Sheet:

    function triggerBuild() {
      var url = "BUILD_HOOK_URL_HERE";
      UrlFetchApp.fetch(url, {method: "POST"});
      Browser.msgBox('Your site is being updated now. Changes will be live in a minute.');
    }

And assign it to an image of a publish button.

Now content editors can work in the spreadsheet, and press "Publish" to trigger a new build and deploy :)