Last year, I received my interview invite around the 1st or 2nd week of August, which is about the earliest that they sent them. So I'd expect those invites to go out around the same time. I think the earliest interview dates were around mid-August when the students got back. So just relax and enjoy the break.
Regarding the letters of rec, I'd have them ready to go out but don't send them until they ask you to. They don't send secondaries (which is also their interview invite) to everyone (only to about 700 applicants). So just have them ready to go out and you'll be fine.