Move to a host that does--there are lots of them. That probably sounds snarky, but it really is the best and easiest way to handle this.
If your host supports manually uploading a certificate, and your DNS provider has a supported API, you might be able to automatically get a new cert every 70-80 days using acme.sh, and then manually upload that cert to your host; that wouldn't be too terribly complicated. But ultimately, your host's user-hostile choice to not support Let's Encrypt is going to preclude a "super easy solution."
Typically, all automation requires web host support or at least requires the host not to prohibit it. As the other replies have said, you're unlikely to find an easy solution with your current host.
We and other people have written software to do this—but your web host has to install it or allow you to install it.