The applications that are ready to be sent to the schools are sent about 4 weeks after the opening day for submitting applications. During that time, applications are being verified (transcripts matched with your data entry). Schools get data dumps on a regular basis through the summer and up until their application deadline. A school may get 25% of its total pool on Day 1. Let that sink in. Day 1, school that will have 6,000 applications has 1500 to read. How long to you think that takes. I'll tell you that it takes me 20-30 minutes to thoroughly read an application. So you have to figure that Day 1 data dump is going to take 500 person hours. Some won't get a 20-30 minute review because they aren't viable candidates but even that may take 5 minutes of somone's time. And there are 4500 more coming in over the subsequent 12 weeks or so.
Your application can arrive on July 1 and not be read until November 1 just because there are not enough eyeballs and enough hours in the day to get through them all as quickly as you'd like. That said, schools pace themselves in handing out interview invitations knowing that they can't use all of their 600 invitations on those applications that arrived on day 1 but have to continually identify the strongest in the pool for the next batch of interview invites. Invitations go out through November at most schools and through February or even March at others.
This is a very long process. Do not worry if you don't have an interview invitation in August, September or October. Don't worry until after the Thanksgiving turkey is put away. If you don't have an interview invitation by Thanksgiving, then you can fret but worrying earlier than that is premature worry because it is just too early in the cycle to figure that it's hopeless..