Start with all civs in contact with each other?

In the Choose Opponents screen, click on the portrait of one of the selected enemies. You should then see, among other things, a slider called Relations. That slider is usually set to Unknown, but you can set it to anything between At War and Team. You have to set this slider for all the races you want to start in contact with.

However, I don't know, if this has any affect on whether the other races know each other from the start, or not.

I just tested this. It even works when randomizing the opponents!

However, I can confirm that the races are not in contact with one another - the "Foreign Relations - Treaties" screen shows them as "Unknown" to each other.

Still, this is a long step in the right direction for me. Thank you very much for pointing it out

I remember that setting!  Somehow, in my earlier exploration in the game, I set myself to "team" with several races.  I was most upset and it took my quite a while to figure out why I couldn't attack anybody I wanted to.  I did leave it at some neutral value and leave it there and forgot about it.   I didn't know that this "know everybody now" wasn't normal.  Now I have to think about it. 

Since the AI empires are not in contact with each other, I feel it gives the player an advantage. The possibilities for tech brokering are phenomenal, but the diplomatic options are also very strong.

The cheat to reveal the entire map gives the AI empires contact with each other (as indicated by the Treaties window). However, I have no idea if the AIs will also have a fully revealed map. If so, then I guess its balanced, except for sensors being useless. If not, the advantage to the player is probably too much to allow a real game.