Can you train a cat the way you can train a dog (or at all)?

We are cat sitting right now and I'm going crazy over the early morning wakings. The cat is very sweet, but he literally ignores us all day/night and hides in the linen closet - fine. But every morning at 5:30am on the dot without fail he is HOWLING outside of our bedroom door until we get up. This cat is loud! And he'll do it for as long as it takes until we get up.

He doesn't need anything. His food and water are always full and fresh (we do this before going to bed), his litter is clean and he has plenty of space to roam around and comfortable places to lay. He doesn't even want to be around us, he just wants us awake. The second we get up and he sees us walking around - he goes back to the closet and hides.

The two cats we fostered previously did this same exact thing. They would meow and howl up a storm at 5:30am until we got up - then they would promptly fall back asleep somewhere. They also didn't need water, food, clean litter or even attention.

How do you stop a cat from doing this - is it even possible?