Database Access from the Managed WordPress website (without plugins)

I have a Managed WordPress website (Twenty Sixteen theme) hosted by GoDaddy and want to access my MySql database from the php script within the custom page template (that I developed). When I try to connect using the code:

<?php
$servername = "localhost";
$username = "username";
$password = "password";
$conn = new mysqli($servername, $username, $password);
?>

I get the error:
Warning: mysqli::mysqli(): (28000/1045): Access denied

I called GoDaddy support and got the explanation that they discourage accessing the database out of the phpMyAdmin environment for the safety reason (if you have the Managed WP), but some people still manage to access their databases. Sure, I asked how and he told me that they are not providing support for something like that. So, is there somebody who can let me know how I can access (and modify some records in) my database (without using some plugin) if I have Managed WordPress for my website? Should I develop some kind of a plugin?? Or I would have to switch to the CPanel account in order to do this (as the GoDaddy support suggested)? Thank you very much in advance for any hint!