There are two online retailers in UK simplygames and shopto. Eventhough UK is a small country where things don't take any more than 1 day to deliver they ship the game 3-4 days in advance to avoid any unforseen delays (and even earlier if it's a holiday period and there's a weekend involved). This also leads to people getting the game a day or two early as a nice surprise.As with anything to do with shipping, it's a crap shoot. They usually try to deliver day of, but ultimately there's no way to be consistent with it.
I'm not saying this is exactly what Amazon US should do, but they could have the items be shipped to the local amazon warehouses in the customer's city itself well in advance like a week early to make sure it's available for delivery on the release date, especially since for preorders they will already be aware of how much copies they have to ship and to where a good few weeks in advance at the least. Amazon likely starts receiving its copies shortly after the games go gold which would be a few months before launch.