“Where in the timeline does the Great Filter occur? “
The Great Filter is... bureaucratization!
It’s destroyed every known civilization that’s been destroyed, and yet every civilization chooses to employ it.
Bureaucratization is the most dangerous power in the universe.
And no civilization can resist it.
I would postulate that one of the points of the great filter would be the ability to leave the planet and colonize another planet. You cant get to CivII until that is possible.
We are not there yet.