Best intro I had was for a Feng Shui game.
Two players wanted to play characters from the Ancient Era (Supernatural Creature, Martial Artist), two from the Modern Era (Detective and Maverick Cop) and one from the Future Era (Techie).
The techie started by being part of a break-in to steal a time-travel device from the Architects of New Flesh facility, they get discovered and a fight breaks out.
The martial artist and supernatural creature started in the middle of a battle to save their school/temple from an attack by the Ascended faction, as the students die heroic deaths, the old master opens a portal to the netherworld for the Martial Artist and Supernatural creature to escape, they jump through it followed by a hoard of angry ninja and beasts.
Meanwhile in the modern world the cops are in a car chase / driving shoot-out following a yakuzza gang.
I switch between the action in each setting mixing fire-fights with fist-fights, and a chase through the netherworld.
Then just as the Yakuzza pull into an ally, the techie holding the time device gets shot at, it activates the device sending him into the netherworld, the martial artist and supernatural creature see this fella appear into front of them to late to stop and they collapse into a heap, triggering the damaged device once more.
In the modern world the 3 from the netherworld, plus several ninja mooks suddenly appear out of thin air above the yakuzza who have got out their car to shoot at the cops who are busy bailing out of theirs.
By the end of the game I have brought a party from 3 different time-zones together.