Just watched Soul, and Joe has what seems to be the Pixar variant of an iPhone X (or any above it, just one that doesn't have the home button at the bottom), so Google's placement of it in 2020 doesn't seem too off.
Judging by the foliage (finally remembered a better word than "flora") it's autumn.
Since a lot of people suddenly end up on the [Stairway to Heaven] I'm assuming it could be COVID? I dunno, it's weird how there were little-to-no people on the stairway, then hundreds, all tightly packed (there was an emo kid there, so I hate to say it, but he probably killed himself based on his archetype and mannerisms. I guess that means it's at least the 2000s, since teenage suicide spiked with Gen Z).
He was in a rap group in school/college, so 2020 is lining up more and more.
22 says she's been "messing with this team for years", as it cuts to the basketball team Knicks missing a slam dunk. Looking at their score history, they didn't play any games in autumn of 2020 (though this is most likely due to COVID, and they would've most likely carried on losing most games.)
The Zone seems to be more in sync with Earth than the Great Before, so I'm going to assume they happen at the same time as events on Earth, not before (like with the Great Before).
They steer away from telling us the date pretty well (and annoyingly).
A very clear numberplate conveniently doesn't have a date on it for some reason.
All this obscurity changes, however, when we finally see a calendar, dated November. It places the movie in 2021, with 2 dates circled on the calendar - November 12 and November 23 - one of these has to be the gig, and the day the movie's set. Looking at the Knick's scores, it doesn't get much better for either of them, but no game was played on either days. Since their scores improve slightly after the 12th, I'm going to put the movie there.
The last few seconds take place the day after, on the 13th.