A good LCP score is achieved by ensuring that the main components of the page can load quickly. This again depends on a whole chain of things, which especially become visible in the waterfall of webpagetest.org.
Think about stuff like handling DNS, connecting, verifying HTTPS, requesting the page, receiving the HTML, processing the HTML and loading other files such as stylesheets, scripts and images. It pays to postpone the elements that are not immediately visible to the user and stuff that should be given priority. To load the other files, it is possible useful to already open the necessary connections if those files are have to come to another place. Think of the connection with a CDN (Content Delivery Network) or third party scripts. Use dns prefetch and preconnect for that.
In addition, it is important that the files are as small as possible. Not just because of download speed, but also because of the time it takes the browser to process them. Therefore, make sure you have streamlined code (HTML/CSS/JS). Do not load things that do not are used and ensure that images are presented in the correct format (i.e. not too small but certainly not too big).
First Input Delay (FID)
The FID indicates how long it takes for the site to become interactive after an initial action of the user. This can be, for example, a click on a button or link. Often this delay caused by the browser still loading other elements. Quoted from webdev:
First Input Delay (FID) is an important, user-centric metric for measuring load responsiveness because it quantifies the experience users feel when trying to interact with unresponsive pages—a low FID helps ensure that the page is usable.