Surprise and stealth seemed to be explained in better detail in the Starter Kit
The Lost Mine of Phandelver features a small goblin ambush (as seen in the WOTC Livestream). The rules walkthrough for the stealth check and the suprise round says to roll once for all the goblins (adding their +6 stealth skill) and compare that one, party-wide check to Passive Perception of the PCs. PCs whose passive is less than the goblin stealth check are surprised and do not act in the first round.
This concurs with the Basic rules where in general one part or the other has the possibility of surprise depending on who is trying to set up an ambush.
1 player/PC scouting ahead of the main party would be treated like a separate party for the purposes of surprise round. They might find some goblins, fail to be noticed by the goblins, slip away warn the party, then the party as a whole could try to stealth forward.
A player showing up late to a fight could be hidden if they make a suitable stealth roll (i.e. some kind of cover) giving them advantage.
In combat, most creatures stay alert for signs of danger
all around, so if you come out of hiding and approach
a creature, it usually sees you. However, under certain
circumstances, the Dungeon Master might allow you to stay
hidden as you approach a creature that is distracted, allowing
you to gain advantage on an attack before you are seen.
If the monsters and the main bulk of the party have already spotted one another/are engaged in combat I don't think a player who is further behind would in anyway get a surprise round compared to everyone else, no matter how good their stealth check. The enemies have already been alerted to the presence of the party (their enemies) and will be wary as the combat commences.
However if that player is trying to sneak into the combat, they can and should get advantage if they make a good enough stealth check.
Short answer: yes, your citation from the PHB supports character initiative or action as the trigger from non-combat to combat.
It's not necessarily "another skill" that can set up surprise, but player actions, preparation, and decision.
Surprising Foes. If the adventurers encounter a hostile creature or group, the DM determines whether the adventurers or their foes
might be surprised when combat erupts. (p. 65, Basic Rules)
Any character or monster that doesn’t notice a threat is surprised at the start of the encounter. (p. 69 Basic Rules)
While the second point is under the "Combat" rules, the surprised condition means that for some or all members of one side, combat actions start later than the other side since actions based on surprise (or lack thereof) are taken into account before any initiative order turn based actions and reactions play out: it complicates the implementation of "roll for initiative!"
If you’re surprised, you can’t move or take an action on your first
turn of the combat, and you can’t take a reaction until that turn
ends. A member of a group can be surprised even if the other members
aren’t.
Two points worth noting:
Surprise can be determined to affect a whole side, or individuals.
From a rules perspective, surprise is explicitly linked to combat in
terms of its significance, which is addressed in detail here.
- If a party is surprised, but no combat ensues, a lot of the detailed
treatment of surprise is rendered irrelevant.
Discussion
Don't let the rules be an obstacle to play
In an attempt to "follow the rules as strictly as possible" in the perspective of "Rules as Written" it is well to also embrace the two other manifestations of the rules in this edition's design as expressed by Jeremy Crawford here.
RAI ... “rules as intended.” This approach is all about what the designers meant when they wrote something. In a perfect world, RAW and RAI align perfectly, but sometimes the words on the page don’t succeed at communicating the designers’ intent. Or perhaps the words succeed with one group of players but fail with another. When I write about the RAI interpretation of a rule, I’ll be pulling back the curtain and letting you know what the D&D team meant when we wrote a certain rule.
RAF. Regardless of what’s on the page or what the de-signers intended,
D&D is meant to be fun, and the DM is the ringmaster at each game
table. The best DMs shape the game on the fly to bring the most
delight to his or her players. Such DMs aim for RAF, “rules as fun.”
The transition isn't all about "roll for initiative!"
The transition from non-combat to combat in an encounter is based on a trigger, an action, or a decision. Your question gets at the heart of that transition, which is often something other than the DM saying "roll for initiative." By setting up the trigger condition, and letting it develop that way, the DM empowers players and ensures their agency (if they do a good job of setting it up and describing the set up/plan, etc). This gets at the fundamental structure of play.
How the game is played:
(Basic Rules, Page 3)
- The DM describes the environment
- The players describe what they want to do.
- The DM narrates the results
Note on point 3: the DM determines results (like whether surprise happens or not), which includes taking into account what effort the players are exerting to set up that condition.
When there is a chance for failure, or when success or failure is an interesting outcome (such as "did we achieve surprise or not?" in your scenario) then any die roll is based on DM Judgment. That is also what the rules spell out. The DM's role includes the requirement to make rulings. The rules in D&D 5th edition are not computer code. They are not a string of on/off switches. They include judgment, which is a human aspect, and which opens the door for a DM to determine "you make that attack with advantage because ..." or "you make that check with disadvantage because ..." and so on.
About terms:
DM Fiat far too frequently attracts a pejorative connotation, which is unfortunate. DM judgment, (and a DM choosing not to metagame but instead role-play the NPCs/Monsters) is what makes or breaks a game.
It isn't a house rule for a DM to act like a DM.
Then the DM determines the results of the adventurers’ actions and
narrates what they experience. Because the DM can improvise to react
to anything the players attempt, D&D is infinitely flexible, and each
adventure can be exciting and unexpected. (p. 2, Basic Rules)
DM judgment is part of the rules. (The infamous rule zero). If a DM doesn't apply judgment, then that role isn't being fulfilled.
Can we do this?
Absolutely, yes. The players characters attempting to lull the NPC's into not expecting an attack, and then suddenly attacking, is the essence of a surprise attack or an ambush, and is their input to the game flow (step 2) once the DM's description of the setting (set 1) is fulfilled.
Which opposed ability checks, if any, are necessary are a function of steps one and two: the DM describes the environment, and the players describe what they are attempting.
If successful, they'll surprise the guards. If not, oops, the jig is up!
Best Answer
There are two ways to interpret that sentence, and it hinges on a weirdness of how English uses the indefinite article.
The usual interpretation of "a threat" here is that it means "one threat". If that is the correct reading, your question is the result. Is it correct though? This meaning would require that surprise is a relationship between two individuals, so that the dire wolf could be surprised by the rogue but also not surprised by the enchanter.
Is this how surprise works? It turns out, no:
Surprise is not a relationship between two entities, it is a state of a single entity. It's impossible to be surprised by one opponent but not surprised by another.
Is there another way to read that sentence about "a threat" that makes surprise sensible as a state? As it turns out, yes.
"English is funny that way"
Another use for the indefinite article, which looks identical to the "one threat" meaning, makes the sentence in question
mean any threat at all, not just one. If this meaning of "a threat" is how it's being used, then that means only creatures who notice no threat are surprised.
Because this reading is perfectly normal English, but ambiguous, we need to confirm the reason by looking for clues in the surrounding text. That confirmation is in the definition of surprise we looked at above: being surprised means being completely surprised, which only makes sense if it happens when no threat is noticed.
So the dire wolf is not surprised, because it did notice a threat, as opposed to not noticing a threat. (See how that makes sense put that way?)
On the plus side, the champion and the rogue don't need surprise to have advantage on the dire wolf, because that doesn't rely on surprise, but rather on being unseen, and being unseen is a directional relationship, not a state.