I think it should start before characters meet. Or during (early on, perhaps), so not all characters are by themselves to begin with, also so they're not all together. Characters and groups can run into each other and either join together or go their separate ways.

Though how hard do you say it'll be to survive? Because I quite like zombie/apocalypse RPs where you have to try [i]hard[/i] to survive - where food and supplies are scarce, and you can't even trust the water (needing to purify it via boiling and cooling before even using it). That would also force people to stick together to survive.