How to speed up Drupal 8 when pages are not cached yet (1st time visit after clearing cache)? D8 has awesome core caching and opens pages very quickly in second-third and so on visits.

But when I clear caches (making design improvements) the response is too long. Very long response during first time page visit in my shared hosting.

I want to move on VPS, so please what to do with my server to speed up drupal 8?
You'll want a crawler (e.g. a cron script running wget) to trigger a local cache rebuilding or some proxy caching solution (e.g. Varnish, CloudFlare) to prevent your server from being hammered on every request upon Drupal page cache flush. Use a crawler if you have a relatively small/fixed amount content and a proxy cache for large/dynamic amount of content.

There really isn't a Drupal-centric solution here. The closest thing might would be the Boost project which has a proxy (local file)/crawler solution, but that's for D7.