Oof, yeah, he's a tiny infant who was taken from his mom and littermates way too young, especially if he's only six weeks now. He must've barely been weaned if he was separated at four weeks. Puppies are typically sent home at eight weeks because they need that time to be with their moms and littermates, to learn from one another and have that attention and security during a critical developmental period. He sounds extremely stressed and scared, honestly. He's definitely not trying to 'get his way', any more than a scared human baby would be trying to 'get their way' by screaming after their entire world was upturned and they suddenly had to spend most of their time on their own. Their physical needs might be getting met, but their emotional and social needs just aren't.
I get that stuff happens, and he's with you now. But you've set yourself up for a much more difficult puppy raising experience than most, and are going to need to put in extra energy and time here. Comfort him when possible. You will never ruin a scared or distressed dog by giving them comfort and attention, despite what many people will tell you. Get him comfortable and happy sleeping through the night with you, and you can always train him to sleep on the floor or in another room later, once he's more settled and confident. Work very hard to make the space you're leaving him in - crate, pen, puppy-safe room, whatever - a super positive space to be in. This may be a case where one of those plush animals you can put warm water in and has an artificial 'heartbeat' may actually benefit, since he can't have mom or littermates to snuggle with, but observe him with it before you leave him with it alone, to make sure he doesn't try to rip it up or anything.
This is not a case where I'd be taking a Petco trainer's advice, because I would not want a puppy this young to be in constant distress. This can have serious effects on their development and their ability to feel safe and confident as an adult. You don't want him to learn the world is scary when he's in this critical period of brain development. If possible, see if you can get a phone consult with an actual behaviorist, preferably one certified through an organization like CCPDT or IAABC (both orgs have a 'find a professional near me' function on their websites) so you know that they have a real understanding of dog behavior and practice working with behavior issues.
I'm just a dog nerd - I like learning about animal behavior, but am far, far from being any kind of working professional - so I don't know what the best option is for you in this scenario. I just know that having a tiny puppy in frequent distress during a period where they're actively learning what is and isn't scary in the world is a bad idea, and his young age will mean you have to approach this differently than you would an adult dog. Just like you'd try different things with an upset and scared toddler than an upset and scared 20-something.