Separation anxiety is normal in little puppies - do NOT listen to outdated advice telling you to ignore a crying puppy. Set things up so your puppy does not experience distress in the first place.
Build security and confidence first, independence will follow when these are in place. That means not leaving your puppy alone beyond their ability to handle that (which may mean not at all in the first days/weeks).
It absolutely IS possible to transition a dog from by your bed in a crate to own bed on floor to own bed down the hall etc etc, and raise a puppy who eventually sleeps where you want, but has free access to where you sleep.
This means your puppy won't cry, won't have a poonami incident in the night, you won't wake up to a shit filled or piss filled crate, you won't wake up to find your puppy hurt themselves or were ill at night, or that there was a gas leak in the kitchen etc etc, because they can come and find you if they need to (and if they're confidence and secure, they will only bother you if they need to).
This only goes wrong when people try to do it too soon, before the puppy has the requisite skills.
The old advice 'start as you mean to go on' is not strictly true either - a puppy has needs an adult dog does not. A puppy is not capable of things an adult dog is capable of. Treating a puppy as if they have the capacity and skill of an adult dog will lead to problems.
I recommend all my puppy clients now get the ZigZag Puppy Training App on their phones and follow the lessons within and use the expert coach chat if they can't get hold of me. It gives access to a real trainer, 24/7, for a very low annual subscription (when I ran in person puppy classes it was part of the course fee!) and sets out reasonable expectations so you avoid duff, outdated advice and have someone to turn to when the puppy blues strike!