I usually purchase the games I want on day 1 , and one of the things I think they need to do on Xbox One is make sure that games are available for download at midnight(for whatever region you are in). Right now this is not the case(not for me here in Canada anyways), some games show up at 3a.m. (eastern), sometimes later.
This is a minor annoyance for me but I noticed something recently that I thought I should share. Usually when the game is out you will see in the the "New Releases" section however it seems that section is sometimes slow to update on launch day, so you can try manually searching for the game in the Store and you may be able to find it that way and start downloading.
Case in point: Sinper Elite 3 is not in the new releases tab now, but if you use the xbox bing search command you will find it and can purchase it right now. (Not sure if I am getting it though....watching a stream to make up my mind.)
edit: oops....looks like that was a bad example, Sniper Elite 3 is in the new releases tab but not at the front(for some reason). Anyways, I remember this working on another game I downloaded recently.