You can use Netlify to deploy and host your static sites.
You can link a GitHub repository that contains the code to your static site to your Netlify account and have the site deployed and hosted.
With Continuous Deployment, Netlify automatically updates your site once you’ve updated the code in your GitHub repository.
To check if your site is running, look over the logs that Netlify provides for each of your static sites.
There are many features that Netlify offer for free but they also offer paid plans for users who need more.