GTY assignments (as well as *GT assignments ), all guarantee bookings can be assigned at any time between the original booking date, all the way up to (and including) embarkation day.
That said, in the past, GTY assignments are generally done 45-90 days out, while *GT assignments are about a week out (usually on a Tuesday).
We've have one GTY that we didn't know our room number until we checked in at the port. And others that showed up anywhere from 10 days out to 3 days after we made the reservation.