In the last two months I have picked up 3 suppressors. First one took 1 month, second took 2 days, third took 2 weeks (including weekends and Thanksgiving holiday). All three were with Silencer Shop single shot trust.
I was told; currently the only reason for a longer than one month delay is due to a couple possibilities: first applicant has been arrested previously and required a closer look. Second, applicant has a fairly common name that is synonymous with a felon in that state or area.
Additionally you must consider the vast increase in applications flowing in now. Long story short: you should be able to take your suppressor home in about a month or less. Most likely much less.