Can’t get JS code to work with shortcode

You need to return the Shortcode generated string, not echo, like this:

function gg_product_front_end() {
    wp_register_script( 'gg_loadProducts_frontEnd', plugins_url( 'js/front_end.js', __FILE__ ), array( 'jquery' ));
    wp_enqueue_script( 'gg_loadProducts_frontEnd' );

    return '<p id="test">Test!</p>';
}

Also, you need to call the JavaScript function, like this:

function gg_loadProducts_frontEnd() {
    console.log( 'Test!' );
}
gg_loadProducts_frontEnd();

Otherwise Test! will not be logged in Browser Console.

Also, check This Post to enqueue Scripts / styles when shortcode is present.