check if .min.css stylesheet exists

Directly answering your question, you should be able use the function admin_url() to get the base URL for the admin folder, and ABSPATH . 'wp-admin' to get the local file path to that folder. Certainly, the WordPress code itself doesn’t expect the admin folder to be named anything different.

However, you should be able to enqueue those styles by style handle (thus forgetting about file_exists() calls) if you do this in your PHP file behind Thickbox:

require_once(ABSPATH . 'wp-admin/admin.php');