My MO for situations like this is to head to the hotel.

I tell the desk agent flat out, "I just landed after a xxx hour trip. Any chance there is a room available? I understand its too early but I'm taking a chance. As noted if there is a Spa/Gym, they usually let you use it. Worst case store the luggage and head to the city.

A few times I got a "Your category of room is not ready but we do have a room xxx and I was offered a very reasonable upgrade price, but obviously one cannot expect this.

Hope you have a great trip.