Ignore all the trolls, it's actually a very simple process. All you have to do is write down the title of the game you bought, the price and the order number on a piece of paper, walk outside and throw it up into the air while yelling "I request a delivery date for my purchase" as loud as you can. I large pigeon will swoop down and take the paper back to GOG HQ, and in a few days you should receive an email containing your game's estimated delivery date.
Hope that helps.
Post edited February 25, 2019 by Hesusio