when i first got milu. i put her in her crate at night. it's a little big for her. big enough to fit her bed in there plus a pee pad. so that's what i did at night. she would sleep in her bed and pee on the pee pad. so honestly, i never had to wake up during the night to let her out to go pee pee or #2.
as for leaving your new puppy in an ex-pen. what i would suggest is putting her bed, toys, food and water in there. and for the rest of the area, cover it with pee pads. you can gradually take away some of the pee pads as the puppy learns that it is supposed to go potty on the pads.