Background Check

I had 2 interviews recently; the 2nd was with a store manager/leader, who mentioned a background check. I did not sign anything during either interview; he just asked if I was okay with a background check and a possible drug test, which I verbally said yes to. He also asked if there was anything he should know about my background, but there isn't. I've never moved and have only had 1 job in the past, as I'm pretty young. Said he looked forward to working with me, and that was all he needed; he just needed to fill out a form to get my background check started, and that I should get an email for it. I called the store today since this was on Thursday, and it is now Monday afternoon, and I hadn't gotten any email. The girl who answered said they didn't send emails for background checks and that I should just wait for a call to go into the store within 4 days to a week; however, I didn't mention to her that I hadn't signed anything. She seemed a bit annoyed and busy, so I'm ngl that's why Im asking on here as opposed to calling again. Is it possible for them to have already started the check without me signing anything? Could they call me in a few days to go in to sign the consent? Haven't received a "rejection email" either, but I don't know if those are even a thing with HEB.