Keep checking, keep checking, keep checking. Depending on where you leave, flexibility, etc. Availability appears to be wildly different airport to airport. I was able to get my family of 5 (only 4 appointments, I already have GE) contiguous appointments on the day we will be at the airport anyway (we have to be there a few hours earlier than we would have been). So it can work, but that was after daily checking and pouncing on the openings as soon as they were available.