Start with a training session. Invite one person for every ten you want to play with. Use that time to try out the game and define and practice roles on how to help facilitate it. There are at least several different roles: you need people to help explain the game, people to help stragglers and strugglers find a group, people to help the groups stay focused, people to answer questions, a couple to take pictures, etc.
Next, with this many people, I'd choose a materials-based game - materials that in and of themselves almost determine the rules. That way, I wouldn't have to worry about everyone actually listening to, and understanding my instructions. For example, lots and lots of cardboard cartons. Maybe 200 or more. If I have a big space to play in, I'd use big cartons. A small space, maybe shoe boxes. And other small boxes. A couple hundred at least. If I wanted to get fancy, I'd take time to paint the boxes before hand, maybe invite some kids who want to get involved. About an hour before the session, we'd start putting the boxes into big piles - probably 10 piles of 15 or more boxes each.
About 30 minutes before the session is actually scheduled to start, I'd start working with my facilitators, making some kind of building-like structure out of one of the piles. And I'd keep doing that with my merry facilitators until people started trickling in. I'd invite them to help us build, of course. As the group got too large for the pile, some of the facilitators would peel off with a few more participants and start building with another pile. And on and on until we all made a village. And then maybe we'd give each other guided tours of our buildings. And then maybe we'd tear them down and combine boxes until we made half as many piles, each with twice as many boxes. And then build again.
Because people'd be talking to each other all this time, focused on the task, and the fun of building, and later the fun of showing, and later the fun of tearing down, and later the fun of rebuilding bigger, I'd feel good about they're having ample opportunity to get to know each other, to experience and express solidarity, to have shared a fun experience upon which they can build a meaningful history. Then maybe I'd move to some kind of open-space technology exercise so that people could express their learnings and leanings.