I'm assuming you mean in the scenario that no one else attacks either. In that case I would argue combat has not started yet. Combat starts the moment the Assassin has decided he's going to attack.
At our tables it goes like this:
DM: The orcs walk down the passage and get within striking distance.
Assassin: I attack the nearest one.
DM: Roll initiative.
If the Assassin player loses and then says: "I stay hidden and don't attack." I would just say "Too bad. You started to move and they noticed you. Next round. They attack." That sort of metagaming is right out the window in my book.
That sort of metagaming evolves if you misunderstand the surprise rules and rule that it ends when the target can react.
Run as I've outlined (surprised until unsurprised = don't notice a threat until they do), if the hidden assassin (and we know that he remains hidden since his Stealth rolls have beaten every Perception roll from the target) declares his attack, roll initiative. It doesn't matter if the target gets a higher initiative, since he remains surprised until he notices a threat. The assassin can attack, knowing that a hit will be an auto-crit; no metagaming needed.
In case you think that this gives too much advantage to assassins, remember that a hit will not only auto-crit (whether or not the assassin has higher or lower initiative), a hit will also mean that the target will 'notice a threat' alright! He will no longer be surprised on that basis, and a second attack on the same turn will not auto-crit.
It's fair on the assassin too, because if he misses but somehow remains undetected (Skulker feat) then the target remains surprised because he still has not noticed a threat, and still vulnerable to a possible auto-crit. If I were DM, I'd have a new Stealth/Perception contest for each attack, and as soon as the target wins he notices the threat and is no longer surprised from that point.
Again, no metagaming needed. When the rules make sense, no problems from metagaming or anything else. If you run it so that hidden people are noticed after a few seconds no matter if invisible/inaudible/scentless etc. (by ruling that creatures are no longer surprised because they have good reactions, even if they have nothing to react to!), then metagaming is only one of the problems that may arise.
The solution to this metagaming is not to arbitrarily rule that the target detects the assassin even when they haven't; the solution is to run surprise the way that makes sense.