So, I sometimes steal a method from Spirit of the Century to accomplish this. It establishes connections between the characters before play beings.
Sit the players down at a table - imagine a virtual table if you are playing online. Give each player an index card, and tell them to imagine that their character's backstory before play was a novel. Write down the title of that novel, and a couple of sentences giving the main conflict or problem in that novel, like the blurb on the back of a paperback.
Now, pass the card to the left. The next player as a "supporting role" in the book. They can ask the main character a few questions so they can understand the gist of the story, and then adds a couple of sentences describing a bit more of the story, and how their character helped (or "helped", if it is that kind of game). Pass the cards again one space to the left, and repeat with a second supporting character.
When you are done each character will have their own novel, in which two people had supporting roles, and will also have played supporting roles in at least two other stories. So, in a table of 5 players, every character has met all the others before play begins.
Then you can start however you want, with the addition that the characters have some sense of each other and a bit of personal history to draw on.