Guy told me the other day (he tracks some forum specifically about this)... 7-8 days.
No personal knowledge, but I was a bit shocked.
I've used that same tracker and it's all over the board. Some 3 weeks, most 10-12 months.
And how ATF goes about it is hilarious - last year, I bought two of them (from the same place) but two months apart.
The suppressor I purchased last was approved before the first one at around 10 months.
There's little rhyme or reason as far as I can tell - par for the course for any government entity.