Multiple attacks against unaware targets

Question

Searching for how to handle all surprise scenarios, I still have one question.
Say that the PC is sneaking up on enemies/enemy and silent-cast Dissonant whispers.

You whisper a discordant melody that only one creature of your choice within range can hear, wracking it with terrible pain. The target must make a Wisdom saving throw. On a failed save, it takes 3d6 psychic damage and must immediately use its reaction, if available, to move as far as its speed allows away from you. The creature doesn’t move into obviously dangerous ground, such as a fire or a pit. On a successful save, the target takes half as much damage and doesn’t have to move away. A deafened creature automatically succeeds on the save.

It is my understanding that initiative is rolled before any attack takes place.
The enemies with a higher initiative would likely end up not doing much on their turn, they still don't know they are in combat (or are we rolling for surprise directly after initiative?).
Then the PC proceeds attacking normally with no advantage, since Dissonant whispers doesn't have an attack roll.
The target is now painfully aware of that he is being attacked. And under normal circumstances, so are his friends.

My assumption is that they are now actively searching for the attacker, as opposed to passively, making stealth much harder. But beyond them moving about and actively searching, no one should know where the attack was coming from, thus not rushing to attack.

Or do we roll stealth again against passive perception, to determine if they are surprised? And if they are, will they wait a turn with trying to actively search for the PC? Or do they just know where he is the next turn?

Answer 1

The way this works is relatively straight forward when we do a step-by-step examination of how the rules initiate combat. So our PC states their intent to cast dissonant whispers on the unsuspecting NPC.

Determine Surprise.

This is the first step for initiating combat. Surprise is determined like so:

The DM determines who might be surprised. If neither side tries to be stealthy, they automatically notice each other. Otherwise, the DM compares the Dexterity (Stealth) checks of anyone hiding with the passive Wisdom (Perception) score of each creature on the opposing side. Any character or monster that doesn't notice a threat is surprised at the start of the encounter.

This is when you check stealth against passive perception. At this point, you have already had the PC roll their stealth check, so you compare that to the passive perception of the NPCs.

Establish positions.

This is probably already done and isn't relevant to the question, I don't think.

Roll initiative.

At this point, no spells have been cast yet. We now roll initiative. Everyone rolls initiative and the order of combat is set prior to any spells being cast or actions being taken.

Take turns.

Now you follow in the initiative order. Surprised creatures cannot move or take action on their turn, and cannot take reactions until after their turn ends.

And once we finally reach our PC's turn in the initiative order, this is when we cast dissonant whispers.

Hostile NPCs will probably spend their next turns searching for you.

If we manage to remain completely hidden, the NPC we used dissonant whispers on will likely alert his allies that something is amiss, and they will begin searching for you by making active perception checks on their turns.