It sounds to me like the large group may have negotiated a late checkout of 3 or 4 pm. If that is the case, you may not be able to check in at 4 pm. What would be helpful to know is how big this group is with respect to the number of rooms in the hotel. If they are occupying half of the hotel, it will take time for housekeeping to clean all the rooms.
You can ask them to offer you something for the inconvenience of checking in later than planned. A $50 per person food and beverage credit is not unreasonable to ask. I have not stayed at any Autograph Collection hotels myself so I know brand standards are not the same as for a regular Marriott or Renaissance hotel. Still, it is not reasonable to just tell a guest to deal with the inconvenience. They booked the large group, and they knew other guests would be arriving the day the large group checks out.