AJAX & PHP | Call a specific PHP function from a PHP file via AJAX?

No, it’s not possible if you want to follow the best practice, and neither you need and should do it.

When you make an AJAX call, some parts or WordPress’s core will be loaded based on the AJAX type (whether it’s admin-Ajax or REST-API). It is vital for this to happen, since some scripts demand on using core functions such as get_the_ID().

Your theme’s functions.php file is going to be loaded in this process. If your file runs some functions by itself, then you probably have to optimize your functions.php, since this should not usually happen, and the functions should be run only when necessary.