You don’t necessarily have to give two weeks’ notice, but you definitely have to give notice. Let your manager know that you’re resigning before they spend any more time on the training process. That way they’re not wasting the time of their trainers and they can start right away on hiring someone else (they should even still have the applicants from 5 weeks ago).
If you’re still in training, your boss probably won’t make you work any longer. If you’re still technically in training, but have been working shifts on your own, they might want you to work a few extra days until they can get someone else to cover the hours, but that’s entirely up to your manager.