I'm looking for a simple & reliable way to host a HTTPS enabled static page on a domain I own. The fist thing that came to mind was S3 static website hosting but there seems to be no way to enable HTTPS for that.
What other alternatives are there?
SSL certificates are issued to the domain it then requires installing via your host or yourself. Shared hosting, the host would do the install for you since you don't normally have the option to do so. On unmanaged services such as dedicated, vps and instances on Amazon you are expected to install software yourself.
Valid SSL certificates are issued by trusted ca companies these normally cost money, once you paid they issue you several unique files this are installed within the OS and not the top level... hence you won't the option since this is your responsibility as a unmanaged service.
So because they are issued to the domain and not the host and require installing is among many reasons they do not provide SSL on hosting. You will need to use a instance and install the ssl, or use a managed vps service or shared hosting if you don't want to install yourself.
There are several options that provide simple static hosting + SSL, some are:
You could also use something like Heroku or S3. These all have varying degrees of complexity (particularly if you want SSL) and cost, although in most cases if you're just doing static asset hosing you'd be better off choosing something other than S3 for ease of use and cost.
Since I work at Firebase, I'll add that Firebase Hosting supports non-SNI SSL (with automatic certificate provisioning), custom domains (even naked domains), is backed by a CDN and has one click deploys and rollbacks.