I think we should just suggest connections multiple characters at a time-- for how they meet, their general attitude, their mutual history--  in this thread.  Players of said characters have the option too decline or agree, or suggest an alternative.  That way we get enough connections so that, even if not everyone knows<strong>everyone</strong>, they at least have a connection.  Then we can agree on a lead up to the DM's first post.  I'm fine with them having worked together before, too.