How to track who has deleted files

WordPress does not log anything natively. Closest it has to such functionality are just post revisions and ability to enable logging of PHP errors.

There are plugins around to log events, but since you hadn’t one installed in advance it won’t help you retroactively.

If you think it was from action by logged in user you might get some information from web server’s HTTP logs, since they should capture requests to WP admin pages.