What about if the surprise attack works only for any character in stealth? First hidden character attacks, then non stealthed characters get brought into initiative like normal, any others in stealth get to make their surprise attack first then added to the initiative order.
I’m not sure I’m understanding this suggestion. I suspect I may just not be getting your point.
But in case I am, let’s take the two alternatives in turn. We’ll assume that our whole party is in stealth, then one attacks, surprising the enemies.
At that point, their attention drawn, the enemy should have an opportunity to spot their attacker and anyone nearby, but for the sake of simplicity we’ll say any other party members forced to make a stealth check succeed, so the whole party remains in stealth except for the attacker.
So the proposal is that combat always starts at that point, and let's say that the “surprising” character always gets first spot in the initiative queue as per mrfuji3’s good suggestion.
We have suggested that all enemies and party members enter combat, roll for initiative and get slotted into the queue, then our initial character gets to complete any other actions and bonus actions (beyond their initial attack) before ending their turn. Any enemies would effectively skip their turns in this first round as they’re all surprised, so what actually happens in this first round is that the rest of our party get to take their actions and bonus actions, with the advantage of starting their turn in stealth as they were hidden when combat started. Our "surprising" character then gets to make their second attack, but by then enemies can take reactions and then combat proceeds as normal.
In summary, in the first round our whole party gets to take their actions and bonus actions with the advantage of stealth on their first attack, and the enemy gets to do nothing.
Is your suggestion that only your surprising character actually joins combat at first? If so, let’s work that through. If they then complete any other actions and bonus actions without you bringing in the rest of your party and you end the turn then all the enemies will get to complete a surprise round but you won’t have chance to bring the rest of your party into the combat as you need to do that on the turn of one of your party, when combat is paused for you. So instead of ending the first character’s turn, you have the rest of your party attack one by one. They get their initial attack with advantage of stealth, then roll for initiative and get slotted into the combat queue, but it’s still your first character’s turn so they can’t do anything else yet. Then once you have all your party in combat, you end the turn of your first party members, and in this first round all enemies just get to gape in surprise while the rest of your party get to make any remaining actions and bonus actions in turn.
What this means is, in the first round, your whole party gets to take their actions and bonus actions with the advantage of stealth on their first attack, and the enemy gets to do nothing.
That is, exactly the same as option one except that you have to manually bring the rest of your party in, there are questions that need to be addressed about whether your party members who stay outside combat are still in turn based mode aligned to the combat (and potential cheese if they’re not) and complications if you don’t bring all your party members in at once and instead bring one in, end the first character’s turn, bring in another and then they roll better initiative than the character you’ve already moved to.
That’s why I think I’ve misunderstood your suggestion! I think you might alternatively be suggesting that subsequent party members might be able to join the combat in later rounds and newly surprise the enemy, which sounds hard to implement in practice. Surely there shouldn’t be a whole other round with surprised enemies, and it’s not clear what it would mean for one enemy to be surprised (do just they miss their next turn?) or enemies to be surprised only by one of your party. And anyway, I would suggest that any “surprise” caused by later party members joining the battle is represented by the advantage they’re getting from attacking from stealth, so adding a surprise turn at that point would be double counting.
Or perhaps I’m still misunderstanding ….