Bootstrapping WordPress MultiSite Outsite of WordPress – No $wpdb

You’ll want to include the wp-load.php, not the wp-config.php.

Depending on how you’re doing it, you may also have to set $_SERVER variables if they aren’t already set to prevent WordPress from trying to redirect you. For example:

$_SERVER = array(
  "HTTP_HOST" => "http://example.com",
  "SERVER_NAME" => "http://example.com",
  "REQUEST_URI" => "https://wordpress.stackexchange.com/",
  "REQUEST_METHOD" => "GET"
);