Hello! First off, welcome to YT! And congrats on your new puppy
I do think you should make her crate smaller. Using towels was a great suggestion. Just pile them up and kinda make a wall near the back of the crate.
What I've done to crate train Luigi (he is 3 months) is to set alarm every once in awhile so I can get up to let him out at night. When I first got him, I was up like every hour just to make sure. Yes, there'll be a few accidents around the house, but it does get better. Now he can hold it much longer, up to 4-5 hours. I haven't tried yet to see if he can sleep through the night. Whenever I do take him out of his crate, I just take him straight to the potty pads. I don't really talk to him or cuddle with him at this time. It's late in the night and I dont want him to think it's playtime. After I bring him to the pads, I say "Go potty" as a command. Then, I praise him when he goes and put him back in his crate ("Go bedtime") to sleep. These commands can be helpful. Sometimes, I can just snap my finger after taking him out the crate and tell him "go potty" and he'll go. No worries, I think you just need to make your crate a little smaller. And be consistent and I'm sure he'll get better with potty training.
Also, to avoid having accidents around the house, anytime I take Luigi out to play or whatever, I make sure to keep a close eye on him at all times. if I can't do this, then he stays in his crate or in his pen (where he has access to his pads). In order to have him follow me (and so I can keep a close eye), I either play with him constantly or put him on a leash and tie the leash to my belt loop (never tug though!) This makes it so that he learns to follow me and is with me at all times if he's out of the crate/pen. He's still too young to be trusted for full run of the house, so that's why I watch him a lot so we can avoid accidents. Sure, sometimes it happens, but just be consistent with your praises and occasional "NO!"s and your puppy will start to get it too. You can start picking up on your puppy's signs that he needs to go too (mine starts sniffing around in circles). When I see this, I take him straight to his pads and say "go potty."
Hope this helps. Good luck!