Amazon has several carriers that deliver well into the early morning hours. I was outside with a sick pup a few mornings ago, and I saw one of the LaserShip trucks in my neighborhood delivering a package. It was 4:30 in the morning.
A few weeks ago my wife was home and a big black Cadillac pulled into our driveway. Out comes a huge man who the wife thought might be there for a mob hit. Then he walks up to the door and very pleasantly hands an Amazon package to her. She still laughs about it.