They start releasing walk in permits the day BEFORE. at 11 am.
"first-come, first-served wilderness permits will be available one day in advance beginning at 11:00 am (not at opening). Wilderness permit reservations can still be picked up the same day or one day in advance when the wilderness center opens. Same-day first-come, first-served permits are also available when the wilderness center opens. This model is similar to the one currently in place by surrounding US Forest Service wilderness permit issuing stations."
Here is what I would do: show up the morning before and get in line. At 10 am they release reserved permits that weren't claimed. Those will be for the day of - the day you are there, you can start hiking, get a jump on the trip, get out a ways and camp. If you don't succeed with released permits, try for the walk in FCFS at 11 for the NEXT DAY. If unsuccessful go to the backpacker campground and stay the night if you can't get a campsite. Come back to the office the next morning and get in line. 10 am, the unclaimed reserved permits for the day you actually wanted to start are released, hopefully that will work. Otherwise just look at what's left and go there instead.
The TM campground has a line early in the morning for walk in sites (50% of sites are walk in). If you can't get one then, you can go on a waiting list. We did this and got 2 sites at 3 pm because people finally checked out and left. That was a Friday. A friend had to do the same thing Thursday before.