Short answer: Wake up in the middle of the night, then walk the puppy out to potty.
A puppy can't make it the whole night without peeing, and it's not good to have the puppy pee in their crate. For one, the puppy would soon learn that it's okay to pee in their crate (plus, it would delay potty training for a long time).
According to the best expert on the subject, the best thing to do is to set your alarm for half-way through the night, then wake up, get out of bed, and take the puppy out. For details on crate training or potty training, see our notes on Dr. Ian Dunbar's terrific book, "Before and After Getting Your Puppy."