Try to push them

In fact, it only need 1~2 weeks for them to collect information and send the application. However, usually they don't do it because there are a lot of cases need to process. It is very normal in University. Those guys are very lazy and they only do limit amounts work every day.

So you need to try to push them do your job firstly. Hope your boss could help you. If you don't, they only put your files at the bottom, and you need wait months to start it.