Fixes: FCP, LCP
This is a very important factor in web optimization and the solution is also very simple. Just use any caching plugins available in WordPress such as W3 Total Cache, or WP Super Cache, etc. along with some CDN services to offload server load on third-party systems like Cloudflare, Cloudfront, etc. You can also use any server level cache as another caching layer to keep the server response time minimum.
If your site is not using WordPress CMS, you can go with caching solutions available with your CMS, or you can still have server level caching, and CDN services like Cloudflare.
There are many caching solutions available, however, it will be wise to monitor and fix the slow mysql queries to not let the mysql load affect the performance of the site. You can add object caching to queries also. This will keep server and mysql load normal.
The page cache layer will help load the page faster once the page cache is generated. So when the first page loads it might take 3 or more seconds to send a server response. But when the page is cached, the server response can be less than 3 seconds, in some cases it can be even less than 1 second.
On the other hand, if you do not use any kind of cache layer, the initial server response will always be more than 3 seconds and then the FCP and LCP will get affected badly.
As you know the FCP is first contentful paint, that means time taken by page to render and display the any of the elements present on the page, it will be always high and when pagespeed insights finds these FCP and LCP web vitals taking always more 3 seconds, it will consider it as “poor performance” or “needs improvement”.
While Google only checks for LCP and not the FCP, it is good for users to know that something is happening on the webpage and the content is loading, that is reassuring users that the page is loading normally and within a few seconds users will get to see full content. If web page starts showing the content frame as early as possible, users are more likely to interact (scroll, tap, click etc.) with the website.