It's very difficult to give any absolute advice - there is no one right way. Like bringing up children, there are those who do controlled crying and those who do attachment.
For what it's worth, I always go to my puppies if they cry in the night. I want them to know that I will always fix things for them, whatever, whenever. I have working labradors and firmly believe that the reason they work so hard for me is because I have never, ever let them down.
I don't make a fuss at night or speak or turn on the lights and I do the same old routine over and over again. Let them out into the garden until they do the wee or poo they were desperate for; give them a gentle stroke and pop them back into bed with a tiny treat. Until the pups have been with us for a month or so, I also warm up their comfort heat as well just to increase their sense of security. They very quickly learn what to expect and settle straight back down again.
Dogs are very, very bright but an 8 week old puppy just doesn't do manipulation. If she is crying, it's because she is unhappy/frightened/needs a wee. She has a massive amount to learn and it's up to you to teach her. Calmly, consistently and with love.
She is too small to manage to go overnight without wees and poos, her insides are just too small and the muscles too weak to hold it in for so long, so the only thing you can do is decide how you want to handle it.
The crate method works well. The crate has to be about the same size as the bed so there isn't a spare bit they can use as a loo and because they are reluctant to mess their own bed, they usually cry to be let out.
I put tiny puppies to sleep in the crate with a heated wheatie, a large soft toy and a bone; gave her a biscuit, shut her in and left her to it. She did cry to start with - but each time she did we let her out and came and soothed her to sleep.
The trouble with not crating is that because he has no-one to ask to go out at night, it's easy for him to hop out of bed, find a corner and do whatever it is he needs to. Crating does mean you end up getting up in the night and wandering round the garden with a torch but it gets you to the end goal of teaching a dog that outside is the place for business sooner.
Mixed messages are not helpful. If you think about it, she's currently getting mixed messages. In the daytime, you're working hard to teach her to go outside to wee and poo. BUT, at night-time, the goal posts move and no-one comes to let her out, you are in effect teaching her it's OK to wee in the house some of the time. She's going to struggle to work out when it's OK and when it's not.
It's a lot for them to learn - and of course, their bodies have to grow enough to physically be able to control it.
If you are anxious to avoid pandering to her every bark and squeak I suggest you set your alarm every three hours during the night and do the silent garden trip routine before she asks you to. Then as she gets older stretch the periods out more and more until she can manage all night. That way she won't learn that crying gets your attention.
I couldn't do it, especially with such a tiny puppy. But I know people can.