Tough call. I know current advice is to let them howl it out but I didn't. I also, now, believe that puppies, like human babies, cry because they are in need and should be responded to. The first night our guy cried I let him go on a bit but finally got up and found he had peed and was lying in soaked bedding. After I took him out (in a winter just like this one in December and it was -30C) and cleaned him up he was fine. He needed out twice a night for about a month, then once a night and he had to pee or poop each time.
I learned two things that night. Don't ignore him, he doesn't cry for no reason. And no more of that small crate to limit him to only being able to stand up and turn around. If a dog or puppy has to bathroom in a crate so small then they are stuck in pee or poop till you relieve them. We kept the crate but the door was always open so he could venture out into the gated kitchen. He still made little noises at night when he needed to go outside to toilet and only very rarely soiled on the kitchen floor, evidence to me that this did not slow potty training one little bit.
Easy for me. I see your puppy continued to fuss. Ours did not. I know some have found they slept beside puppy for about a week so they could reach him and touch him to reassure him in the night. Good luck.