Is it possible to invoke cron within a hook or route class?
The reason why you get that error is because run is not expected to be called statically. \Drupal\Core\Cron is a service class managed by Drupal, registered in core.services.yml. To get a reference to the instance of this service, you'll need to inject the dependency to your controller.

namespace Drupal\mymodule\Controller;

use Drupal\Core\Controller\ControllerBase;
use Symfony\Component\DependencyInjection\ContainerInterface;
use Drupal\Core\CronInterface;

class MyController extends ControllerBase {

  protected $cron;

  public function __construct(CronInterface $cron) {
    $this-&gt;cron = $cron;
  }

  public static function create(ContainerInterface $container) {
    return new static(
      $container-&gt;get('cron')
    );  
  }

  public function myPage() {
    $this-&gt;cron-&gt;run();
  }


To call it from a hook, if you'll need to use \Drupal::service() to get a reference to the instance:

$cron = \Drupal::service('cron');
$cron-&gt;run();


A full example of how to manually run cron can be found in the implementation of the Cron settings page (Configure -> System -> Cron). In that page, you have a button to manually run the cron. See the runCron method, which is attached as the submit handler of the "Run cron" button.