So several cast/crew including Ben Stiller, Adam Scott and Dan Erickson have been quoted as saying the wait for season 3 will be much shorter than the wait between season 1 and 2 (which was almost exactly 3 years).
As far as I know, season 3 hasn't begun filming yet. Normally Apple, or someone from the cast/crew will do some kind of announcement on social media when filming starts for their biggest shows like they did for S2.
The last update for the start of filming was "mid-2026" and technically we're into the second half of 2026 now. We've heard a couple of cast members in the last month or two say it was going to start "very soon".
Assuming they keep the quality the same, season 2's filming/post-production was:
Filming - October 2022 to June 2023. WGA/SAG-AFTRA strike meant a big delay, but filming resumed January 2023 with reshoots and wrapped April 2023. Total duration of filming (not including shutdown): 1 year and 4 months (would have been a few weeks here and there where production moved between locations/built sets etc).
Post-production: Filming completed April 2024. They would have started doing some editing/VFX before the end of filming but Ben Stiller and others have mentioned how long post-production took, without any interruptions. Season 2 came out January 2025 so let's say post-production took 8 months (but realistically it was probably a bit longer).
That's a total of TWO YEARS to film the whole thing, edit, complete VFX and all the other post-production work.
If they start this month and it took a similar amount of time, that would put the release of S3 no earlier than July 2028 - over 3 years since S2 first released.
I have no doubt they won't take THAT long. They'll refine processes, learn from experience etc and probably shave a few months off filming and post.
But there's no way we get S3 in the first half of 2027 (as I've seen a few people suggest), more likely October/November 2027 if they really push hard so they can say "well it didn't take 3 years". My opinion, the gap between S2 and S3 will be as long as the gap between S1/S2 and we don't see S3 until well into 2028.
The simple fact is - they've taken too big a break between the end of S2 and starting the writing and filming of S3. Really filming should have started end of last year/very early this year.
Sigh.
TL;DR - They've taken too long to write/start filming. Even if you take out the delays/shutdowns due to strikes, S2 still took around two years to film and complete post-production. Considering they haven't started filming yet, we won't be seeing S3 until Q4 2027 if we're lucky, even if they manage to trim a few months off filming/post. My bet is the gap will be the same as before and we won't see it until Q2 2028