Immediately in Toy Story 4 we see concrete evidence as to where the flashback and main events take place. It states that the flashback is "9 years ago" and has a September calendar starting on Tuesday. Going 9 years back from 2005 (1 year after Toy Story 3) then going one year ahead from there, 1998 lines up with the September calendar, placing the main events of the movie in 2007, 3 years after the first. This makes Bonnie 3 in Toy Story 3, not 4, as is commonly believed. There is also a numberplate that appears to say February '99, though it's blurry in all the rain and appears to most likely say '10, which would be completely incorrect anyway.
There's no calendar for the first clip in the montage, though the second one is dated to August, 2000, making Andy 12, so he could still be playing with toys. Young Andy appears to be the same age throughout, so I'm going to assume they're close together, in the same month at least. It then cuts to college Andy giving Woody to Bonnie, which appears to soft retcon the ending of 3, though it could just be a retelling. It appears that the next clip takes place just after Andy leaves, as Bonnie's toys are strewn in what appears to be the same positions. There's nothing to help with the next clip, though the one after is Bonnie in a pool ring and snorkels, so I'll assume it's just after they get back from Hawaii. After this, there's no more indication, though it highlights that Woody now has "Bonnie" written on his foot, implying it's new, so I'll put this in January 2005 with the Snorkel clip, and the one before snorkels before Small Fry.
An older version of Boo can be seen in Bonnie's classroom, however since this was deconfirmed as being Boo, I'm assuming the one that appears in the carnival is a more accurate depiction of older Boo (it was never clarified if this was or wasn't Boo).
Dad says "Kindergarten doesn't begin for another week" (on day 1) and I'm assuming Orientation would begin a week before, not a day that could be said as a week.
The RV's numberplate says Jun 19. This cannot be the case, since Bonnie hasn't aged much since Toy Story 3, in 2004. I am assuming June 2019 was the month the added the numberplate, and not a conscious decision.
Not necessary for any timestamps, but Bo Peep says she's been lost for 7 years, meaning she was owned for 2 years after Molly, then in 2000 was lost. Billy, Goat, and Gruff also bring the Grape Soda badge to Bo (from Up) but I'm disregarding it as a true connection, since it's just a bottle cap.
Duke Caboom is based on Eric Knievel, who had an action figure release in 1972, and a stunt cycle in 1973. Since Rejean watches an ad for Duke, and there's a Christmas tree, I'm placing this flashback on December 25, 1973.
The credits have a few mini scenes, all taking place one after the other, on the same day/day after Toy Story 4 (Day 2). After this, Jesse says it's Bonnie's first day of 1st grade, so a year has passed (I think? British, I don't know how long Kindergarten lasts)