Is there data out there about how recently one must have raided at a specific to be eligible for an EX raid invite?

https://pokemongohub.net/gym-raid-update/comprehensive-guide-trigger-ex-raids/

https://www.reddit.com/r/TheSilphRoad/comments/7ojuoi/how_to_determine_which_gyms_are_eligible_from_ex/

unfortunately no there is no data.
the sylph road questionnaires don't seem to contain questions that would lead to this data either.
and as you can see above many people misunderstand the question.

as best as we can tell your best chance is to raid within the 'cycle' since the previous ex raid were announced, but to be safe i would say in about the 3 days before the next passes are due to be handed out.

I know of a person that did one raid in a park that is our best chance at an EX pass...and got invited.
It would appear that one raid is enough to get your invite...it just has to be the right one.

The rest is RNG.