As soon as the carpet arrived at the house, I took it out of the box and laid it out flat in the basement. It's been laying there for weeks. The rear section fits really well, except for a couple tight corners where it's wrinkled up. By putting in the sun for a few hours, you should be able to push out most of the wrinkles. For the more stubborn ones, you can use a heat gun (very carefully) to warm the wrinkles and then press them out.
The front section of the carpet is going to need more work then the rear. The heel pad has a pretty good crease in it from being stuffed in the box. Hopefully most of it will come out in the sun. I can smooth it out the rest of the way with a heat gun.