I try to have each character know at least 2 other characters in the game, this creates some overlap.

I ran a game (and after almost 11 months) finished a campaign with a bunch of teens who had never played any RPG of any kind prior to this, and while making characters they created a traveling circus or carnival kind of thing and every character had some ties to it. So even when they did not know one another they would see the troupe's emblem and become instant friends.

The other method I enjoy is trial by fire, starting the game with an intense situation and they have to work together to survive. I used this to start the other d&d game I am running. It also inadvertently happened when I was introducing two new characters to my Werewolf The Apocalypse game.