Call AJAX callback on page load
Funny how those tutorials did not mention Drupal behaviors, which will trigger once the page is loaded. This is a good tutorial on them (Drupal 7, but same principles apply).

Basically all you should do is call your callback function from a behavior to get the same effect as jQuery's document ready callbacks.

Drupal.behaviors.myModule = {
  attach: function (context, settings) {
    // Call callback here.
  }
};


And while you are at it, I recommend reading up on behaviors as they help to streamline your javascripts and keeps them in closed scopes.