I know this is a very stressful experience for anyone who has gone through it, but honestly, I had no idea how bad it really was. My daughter has a 4.0 in Biology from a strong state University, she got a 36 on her MCAT, she has been doing cancer research for 2 years, she works in a doctors office, and she worked for her college. She is well spoken, attractive, but as a white middle class student, I am not sure if she is going to catch the eye of admissions counselors. She applied to 22 medical schools, got 22 secondaries back and just got her first rejection from University of Wisconsin. She has not gotten any interviews yet and completed most of her secondaries about a month ago. How long does this typically take? She is applying to some very competitive schools, not ivy, but Vanderbilt, Johns Hopkins, Mt. Sinai, etc. How many do you think will offer her interviews? What are her chances? When will they start to inviting her for interviews???
Let me offer you my sympathies. I’ve been in your shoes twice. (2 daughters–one in residency; one a MS2. Both, BTW, middle class white girls.)
There is a thread in the pre-med forum for students and parents of students who are applying this cycle.
This process is long and humbling. It’s mentally and emotionally exhausting. And requires great patience. (And adult beverages PRN. 
)
Interview season lasts from mid-August until mid-February at most schools, with the bulk of interview invitations going out before Thanksgiving. Neither you nor your daughter should panic just yet. There’s still time.
It’s impossible for anyone here to make a guess about her chances, or when/if your daughter will receive any interviews because a med school admission requires so many soft factors besides GPA/MCAT/some research experience. We are not privy to contents of your daughter’s LORs, nor know what other kinds of activities she has besides research. We are not in a position to judge the quality of writing skills or how well she has presented herself through her essays. Nor are we able to see how well her overall portfolio matches the mission of the schools she applied to.
It may be helpful to read this AAMC paper–Medical School Admissions: More Than Grades and Test Scores
https://www.aamc.org/download/261106/data/aibvol11_no6.pdf
Many of the med schools your daughter has applied to admit fewer than 5% of applicants. Applying to only top schools is a very risky strategy.
I agree you’re fretting too soon. Admissions is a rolling schedule. Schools will interview/offer; student may turn down since s/he got in elsewhere. School may reopen interviews, and so forth. Some of D’s friends did not get offers untiol very late in the process. Calmness is recommended. Hard it is, says Yoda. Know that do I. 
Are you Wisconsin residents? If not, I’m not even remotely surprised she was rejected.
Way too early to start worrying.
I went to med school with people who got in off the waitlist 4 days before orientation was to start.
But to echo what WOWMom said, only applying to top schools is risky. The goal is to be a doctor, not a graduate of ******* Medical School. It’s late, but there may still be time to put out one or two more applications to less competitive schools…
I am curious about OP’s designation of Johns Hopkins as being not an Ivy and so a tier below…
There was a time when JHU was the number 1 medical school for several years in a row and is still ranked number 3 after Harvard and Stanford. There are some ivy medical schools ranked in mid 30s even now. The other two schools mentioned are both top 20 schools.
Agree with IWBB about Wisconsin. It seems to have 77% in state students.