So I found this article.
AMP is a pretty engaging sci-fi short written and directed by Adam Marisett for Triton Films. It's set in a world where giant robots can be your best
gizmodo.com
In it they discuss when the Werewolf By y Night special takes place. These are the quotes of note:
io9: "And we don't even know when this night is. It could have been in the 1940s. It could have been in the future. We don't really know."
Giacchino: "That's the great thing. In my mind, it is happening somewhere within the MCU but we purposely never say when, why, how, all of that, because to me, it was just about these characters. Let's worry about these people for tonight and see what happens."
So seems like there's not going to be anything particularly useful to pinpoint the time placement. It'll probably be down to Disney+ or some obscure hints and details.