If you meant the Jekyll support build into GitHub, you could use a free CI service to run any other SSG, and push it to GitHub pages or any of the other suggested solutions. If you want everything from one service, GitLab uses their CI service for GitLab Pages and have prepared templates for many SSGs already.
GitHub Pages (https://pages.github.com/) is another popular option but it only supports Jekyll, and if you wanted a CDN, form handler, redirects, and other features then you'd have to tack on other services.
I have a CloudFront distribution sitting in front of S3, secured with a free SSL certificate powered by Amazon ACM.
I like S3 for its flexibility. My site is in both English and Dutch and I want to serve English content on .io and the Dutch content on .nl. With S3 I just create two buckets, associate the bucket with a different domain and welcome page (index_en.html and index_nl.html) and publish the same site to each bucket.
Integrated with Bitbucket, git push deploy, Docker auto-builds of static generators, wildcard SSL custom domains, CDN, etc.
disclaimer: I work at Aerobatic
Then if your site becomes famous - drop cloud flare in front.