On the cpanel server, any good caching method?

The cPanel server limits some caching options; however, there are a wide variety of options available, but depending on the main problem of the first-to-byte response, you would probably see those options first.

If you are looking to speed up the response from the cPanel server site, the LiteSpeed ​​web server is a great update to keep in mind with the included caching, possibly a nginx update if the cost of low speed is prohibitive.

PHP opcache is another thing that should not be omitted and use PHP 7.

memcache and redis is another thing that is worth looking at also if the site code can work with that.
We have also obtained excellent results with the varnish, but its configuration is not so direct but it can be done.

If the use of the MySQL server update to MariaDB can also bring some performance improvements, it all depends on your use case, not to mean also configuration optimization.

Making sure that gzip compression is enabled, browsers cache static content, and css / js files are minimized to save transfer time.

As @mhostingin The Cloudflare with meaning or another CDN network for its static content will probably also have an impact.

Here there is very little information on what site it is, but those are some of the options that you can examine yourself. If you are still not satisfied with the performance, it may be worth hiring a system administrator to review the performance of your server and its optimizations, it is also worth asking your hosting provider.
I could have some suggestions for your current use case.