My guess is it is many thousand deep right now. There are still people who interviewed in April and were told they would be hired who haven't started yet. The LOR is probably vital to get the interview now, but they are not interviewing right now and they haven't said when things will start up again. I'm not trying to discourage you from applying- get it in with the LOR as soon as you meet the requirements, but don't expect to here anything in the near future. Good luck. It will be worth the wait.