Can’t log in to new iMac—mouse won’t connect

I have a new iMac I’m in the process of setting up for the first time. We have 3 user profiles. Hit a complete standstill for the past week: on the account login screen, the mouse won’t connect. Forcing restart just brings me back to the same spot, and the cursor is stuck in the corner, so I’m unable to select a profile to log in. I rebooted in safe mode, but because the mouse won’t work, I can’t select anything from that screen, either.

I’ve tried connecting the mouse to the lightening cord to charge it, tried turning it off and on… seem to be out of options from there.

Any way to force the keyboard on the login screen? Any way—without a mouse—to wipe the entire thing so I can start over?