My experience as well--First appointment was some months away, I took what was available.

But in subsequent weeks, more slots opened. I was unable to shift to these, but for a busy place like LAX TBIT, it was nice to see that it's worthwhile checking every few days or a week.

I'll also say that others who applied had learned of other offices in metro Los Angeles--the list includes The Usual Airports, but there are a few which are labeled with rather obscure information. One person made an appointment at an office in Culver City.

So if you want as early as possible, look carefully at the list of offices/venues, and test out anything that looks possible--even mystery codes--you can always change/cancel if it turns out to be somewhere across the country.

I'll add that the officers at LAX TBIT with whom I spoke (front desk and interview) were patient and good natured.