At the end of the day each tribe (still not knowing about the other tribe's existence) has to vote off one person. Each tribe meets at separate times for tribal council, and the one person is booted off from each tribe.
As the remaining players are feeling smug and confident that they survived the first vote, Jeff then says to each tribe "now you will all vote again right now,to vote off another tribemate". He does this 5 more times, one at a time until each tribe is down to 9 members. (I know this would be hard to do for television)
That night each shocked tribe tries hard to scramble to understand the fact that they are already down to only 9 players and wonder what the frikken hell is going on. The situation will make them both feel a bond with each other and be suspicious of each other the entire night. None of them will sleep well, if at all, and the fireworks will be great entertainment.
They next morning with little sleep the two tribes meet and find out about each other and the game is on. They immediately get a physically demanding reward challenge, which is for a nice final meal, some blankets and tools.
Now that's the kind of high stress that would make the start of Survivor fun to watch!
You should send that idea to the producers! I would love to see it.