How Can I Expand the WordPress Customize window without any Plugin?

You can expand the WordPress customize area without plugins by applying a simple line of CSS.

.wp-full-overlay-sidebar {
   width: 30% !important; /* The width of the customize area */
}
.wp-full-overlay.expanded {
  margin-left: 30%; /* Here would be the width as same as the customize window width you set */
}

Hook the CSS to admin_enqueue_scripts() function to load it in the WordPress customize area.
The CSS file enqueueing example is given below-

add_action('admin_enqueue_scripts', function() {
   wp_enqueue_style('your-prefix-admin', get_template_directory_uri().'/assets/css/admin.css');
});

Note: This code should put into your theme’s functions.php file. You should create a file named admin.css in the assets/css directory (create the directory if it doesn’t exist) in your theme.

For child theme, you should the get_stylesheet_directory_uri() function instead of the get_template_directory_uri() function.