How you deal with it depends on you and the doggie. It will get better.
My friend has a puppy and she uses a toy that she got at Walmart that has a heart beat. It is a regular baby toy. I have two puppies right now. Each puppy has their own crate. The first few nights they cried and I used a sound machine set on the heart beat sound, they had to get used to sleeping alone. I don't think that is why your puppy is crying to get out. I think he is crying because he wants to be with you.
Try taking him for a brisk walk so that he will be tired. And try to prevent him from taking long naps in the evening. I know after working I just want put my feet up and rest. But Puppies need to be busy so they will be tired at bed time. You can even sit on a chair and toss a ball for him.( My neighbor does this from his wheelchair. He has a Minpin and they play every evening. It is so cute.)
You can teach him QUIET during the day or evening. When he barks say QUIET and Reward when he is quiet, with a tiny rice sized treat. You can do this when he is in his crate at night. Say QUIET wait a few seconds for him to be quiet and reward. Still take him out on a leash before putting him to bed and about 6 hours later he prob. really needs to pee again. My puppies are almost 6 months old. I put them to bed at 11pm and they wake me about 6 am. My Adult Yorkies wait until I get up around 8:30am.
I must be honest, one of my Yorkies sleeps with me. I got her as an adult. She was not crate trained. She barked and whined in terror. I opened the crate to take her out, thinking she might need to pottie. She jumped on the bed shaking. I talked to her quietly, she stopped barking and made a little nest. She has been in my bed since. Hope you get a good nights rest soon.