Cannot set cookie on init hook

I have a weird problem when trying to set a cookie with the init hook (I must say I’m new on WP)

This is the code that’s not working:

plugin.php file:

...
require_once( PLUGIN_DIR . 'class.plugin.php' );
add_action( 'init', array( 'Plugin', 'init_hooks' ) );
...

class.plugin.php file:

class Plugin {

    private static function init_hooks() {
        ...
        add_action('init',array('Plugin','setCookieAction'));
        ...
    }
    public static function setCookieAction(){
        setcookie('mycookie', $_GET['myCookie'], time() + 3600, COOKIEPATH, COOKIE_DOMAIN);
    }
}

However, if I modify the class to this:

class.plugin.php

class Plugin {

    private static function init_hooks() {
        ...
        setcookie('mycookie', $_GET['myCookie'], time() + 3600, COOKIEPATH, COOKIE_DOMAIN);
        ...
    }
}

The cookie is being set.