Have you tried to put a blanket over the crate so the puppy feels cozy and safe and maybe a radio on for background noise, if it is too quiet in the house at night some puppy listen for noises and then react to them thinking it is you coming down to see her. As long as you put her out just before you go to bed and she have done her business, then put her straight back into the crate and dont make a fuss over her, then walk away, give the praisies in the morning when you first see her to put her out,(early). It will take time for her to get used to it as she is only a baby and will be missing her siblings and mother. Have you tried to put in a jumper or top that you have worn so it have your scent on it, and place that into her bed, she may sleep cuddled into it.? If you keep coming down to her every time she cries she will get used to it and keep doing it. Try to ignore her. You can sneak down and do a sneaky look but dont let her hear or see you, that way it puts your mind at rest that she is ok. If she still wakes at 4am then you could take her out for a pee etc then put her straight back in and leave her. I put a puppy pad in my dogs area's (I didnt use a crate) but I limit an area for sleep in the room.
