You can do this using jQuery.
First of all, you need to add your script into your functions.php
function my_theme_scripts() {
wp_enqueue_script( 'expand-tags', get_site_url() . '/js/expand-tags.js', array( 'jquery' ), '1.0.0', true );
}
add_action( 'admin_enqueue_scripts', 'my_theme_scripts' );
Then, in your file (expand-tags.js
) which is located on, for example, public_html/mysite/js/
, you will have to have something like this:
$(document).ready(function() {
$("#link-post_tag").trigger("click");
});
link-post_tag is the ID of the Choose from the most used tags button, so when the page is loaded, a button click will be triggered.