I think Monster Inc world is actually after the movie

[Alchemike 48]

If you see the enviroment and how Sully and Mike acts,they seems rather familiar with her like Mike says "c'mon boo,im Mike wasowski" they feel like they know her.But the prove above all are the room where they works with the doors are full of balloons and you know when balloons are in monster inc.That's right during the ending.So the kh3 events are basically shortly after the first movie.

[somedayhunchback 213]

Set after the movie. Like the story will be set after the Big Hero 6 movie. (So the Kingdom hearts story won't affect what actually happend in the movie itself). 

[Master Keeper 687]

They’ve already made their farewells to Boo at the end, so it would be weird for the game to occur after the movie

It’s like Mike “bye Boo”

Boo “bye bye”

....Minutes later.....

Mike “oh hi Boo! We are back!”

[Felixx 6,646]

The motto is “We scare because we care” though, so I don’t think it will be after the movie. Also Mike and Sully got to know Boo during the movie so that’s no valid point imo.

[Vaikingu 34]

I see your point.

if you look closely. you can see balloons at the work place when they have to go inside the Doors. wich could look simliar to the end of the film.

[Danjam 2]

It's almost definitely set after the events of the film. At 1:53 in the trailer you can see a sign on the wall that says "Be Funny" referencing the fact that it was found at the end of the film that laughter is a better source of energy than screams. And at 1:07 you can see scaffolding in front of the "We Scare Because We Care" motto to indicate that they're in the process of updating it.

[Alchemike 48]

i know it's strange that boo is there but remember that the organization brings back the baymax left in the portal.So it's possible that it is set like really closely after monster inc. ending (perhaps even at the same day of the ending) and at that moment vanitas came to create problems with the doors bringing back boo.

[Connected 978]

I also think it's after the first movie. In this mission here we see we need Boo's laugh power, which they also start to collect at the end of Monster Inc movie instead of screams. 

[ocean's rage 772]

there does seem to be some evidence to suggest that, i wonder what the story would be like

[Terranort9406 288]

Probably the balloon gameplay and Vanitas cutscene it's after they save boo, and the laught bar it's to open doors just like the movie when they scape from the villian.

[Jingilator 922]

I know this is massive amounts of late, but just for anyone confused: the last scene before the credits roll is Sully opening Boo’s door and seeing her, which opens the possibility that Monsters Inc. in KH3 opens sometime directly after that.