Change the CSS of the Customizer API

Definitely, you can use the customize_controls_enqueue_scripts hook to load custom CSS and JS.

This is an example of making the panel 400px:

File: sample-theme/css/customizer-controls.css

.wp-full-overlay.expanded {
    margin-left: 400px;
}
.wp-full-overlay-sidebar {
    min-width: 400px;
}
.wp-full-overlay.collapsed .wp-full-overlay-sidebar {
    margin-left: -400px;
}

File: sample-theme/functions.php

/**
 * Enqueue style for customized customizer.
 */
 function sample_theme_customize_enqueue() {
     wp_enqueue_style( 'custom-customize', get_theme_file_uri( 'css/sample-theme-customizer-controls.css' ) );
 }

 add_action( 'customize_controls_enqueue_scripts', 'sample_theme_customize_enqueue' );