Hi, I've stayed at the HIE Pride Park a few times probably a 5-10 min walk to the station, assuming the Roundhouse entrance is open. Never arrived that early, but given there's a car park at that entrance/exit, I cant see why it wouldn't be open at that time. Especially as there's a few hotels located on that side of the station.
Pre-Covid, I started staying at the Derby Midland BW hotel, which is about 70 yards from the main entrance on the left. Lovely hotel with a great breakfast, although last time I looked in May 21, they were not accepting reservations.