I adopted two sibling puppies in the weekend and I'm having tons of trouble with one of them. Due to a bad first night experience, she realized that whining works and has been constantly whining ever since. I'm crating them and that's been working pretty well. I've progressively let them alone in the crate for more and more time and now they are already handling 45min-60min pretty well. However by the end of the day sometimes she starts whining and I don't really know how to handle it without showing her that whining works. Can I wait just a couple of seconds after she stops whining to give her attention? I realize that this is all new to her so I don't want to overdo crating, but I don't really know how to handle that
As you correctly realized, whining is a call for attention and every positive experience (getting out of the crate) will be connected with it. You have no way to tell a puppy "No, I don't let you out of the crate because of your whining, I let you out because you waited long enough".
In my experience, waiting until the dog stopped whining for a few seconds doesn't work either, because the dog's mind is still in an attention seeking mode. They might have the restraint to stay quiet a few seconds (or whine in a pitch you cannot hear), but they still expect you to react to their whining.
What works better is to distract the dog from their whining and put their mind in a different mode. A very good method is to do very simple obedience training with them still in the crate. Sit down, follow me, turn in a circle and suddenly the door opens. That puts your dogs into an obedient mind set instead of attention seeking and it rewards them for their obedience at the same time.
If your puppies are too young to know those commands yet, you can easily teach them to follow your hand or a toy or snack.
Another variant mentioned by UIO is to give them a chewing bone or similar snack that takes a while to eat. That allows the dog to focus on the snack and calm at the same time. Let them out when they're finished or simply open the door while they're still chewing.
It's crucial to change the training sequence each time, even if only for a little bit. You should avoid teaching your dog that turning in circles is a substitute behavior for whining. That only leads down the road to obsessive compulsive behavior.
Be aware that a command like "lay down" or "stay" is ineffective for stopping the whining of a dog. Commands only work if they are connected to a positive outcome. If you tell your dog to "lay down and shut up" and then turn around and walk away because crate time is not over yet, the command loses it's effectiveness because it's not followed by a positive outcome. Your dog might eventually ignore your command just like you ignored their obedience.