Font awesome needs two things.
The external CSS.
Use of classes.
See https://www.w3schools.com/icons/fontawesome_icons_intro.asp
A very basic approach is to copy and paste that code on any page like index.md
It doesn’t matter if your CSS is not in head, just get it to display as a first attempt.
After that works, then you can look at doing it the right way with CSS in the head tag.
It would be useful to have a link to your actual theme or repo
But the general idea is you need to find where the head tag is defined in maybe default.html layout or includes/head.html
If the theme already has one of these, you should copy the file from the theme to your own project as is and add just the one CSS line you need.
Then you can use the FA classes anywhere on your site