nowhere, everywhere...
. this is going to meander a bit.. so stay with me 
we all know that initiative is rolled at the start of an encounter. "surprise" is in delaying the start of an encounter until conditions are most favourable to your side.
Initiative is also now determined by different skills based on what you are doing - eg. if you are sneaking, you would roll stealth instead of Perception. this implies that the actions you were up to prior to entering hostilities in many ways dictates how you will respond (and how fast you will react), once initiative is called.
the GM also has the ability to apply bonuses to Initiative based on the actions the PC's or Monsters are doing just before Initiative has been called.
per the CRB pg 468. "Rolling Initiative marks the start of an encounter. More often than not, you’ll roll initiative when you enter a battle."
so you DON'T want to enter battle until you want to enter battle. Surprise here is determining (when possible) when to start a fight. in the GM section, calling initiative is the transition from Exploration mode into encounter mode.
but the key KEY element is on pg 498 Rolling Initiative: "Call for initiative once a trap is triggered, as soon as two opposing groups come
into contact, or when a creature on one side decides to take action against the other."
holy crap, long winded way to get to my point
worth noting, save for one little side-bar on pg 499, there is no use of the word surprise anywhere for combat.
so, here's how my group has interpreted all of the above. Combat starts "as soon as 2 opposing groups..." or "when a creature on one side decides to take action..." the key here is to either not be perceived as an opposing group or to not force a decision to take an action until its on your terms. how is this done? entirely through your actions in Exploration mode prior to the start of combat.
Example 1: kick down the door, rush in. monsters automatically perceive you as an opposing group, initiative is rolled as soon as the door fly's open. you are at a (possible) positional disadvantage because you are at the door and will need to move a certain distance to get within striking range of your opposition. this costs you actions that could be otherwise allocated for other purposes.
Example 2: same door, you hear the monsters, some of the party sneak, and some are going to try and bluff their way into the room. door opens, monsters sense motive and seek - and discover something is amiss. at this point, same as example 1, you instantly transition into combat by calling initiative and PC's are at positional disadvantage.
Example 3. same as 2, but PC's pass all their exploration actions. monsters are completely oblivious. the sneaky sneaks are sneaking, and the deception of the pizza delivery is working. the PC's move into the room, they slide into position. Pizza Delivery folks get themselves into Flank position ahead of time, or close to the rooms BBG - whatever. Monsters are, like, "sure whatever, we love pizza!" and depending on what the PC's are doing, there may be other sense motive or seek what's going on. maybe not. until the PC's are ready. the PC's "spring the trap".
now, initiative is rolled exactly the same. Order is figured out exactly the same. 3-actions are exactly the same way, with the following differences. nobody gets a "surprise round". this doesn't exist
now, you'll notice the flaw (if you think in a 5e mindset). rolling initiative as per normal, you or your side has no "guarantee" of going first. this is 100% correct. You better be using those stealth and deception skills that you are really good at to try and get into position (otherwise, you will likely have been caught earlier), but this is the vagaries of life and combat. there is no guarantee that the ambushing side will universally act faster. there is nothing to suggest that a monster may notice that slight twitch in your eye and they react quicker. the only thing you can hopefully do is decide when the fight will start, using the skills/abilities you have to give you the most advantage to try and go first - but once it starts, its all up to luck.
some may say this is not "Surprise" in the traditional sense. I 100% agree, but what I LOVE about this is the positional aspect of the lead-up to combat. if you can start a fight when you are flanking a foe, just due to the action economy, you have given yourself in the 1st round a huge advantage...
Anyway, that's how my table has interpreted things, and I honestly love it.
(now I'll grab some popcorn and wait to hear how stupid we are
)
cheers,
J.
couple quick notes:


we all know that initiative is rolled at the start of an encounter. "surprise" is in delaying the start of an encounter until conditions are most favourable to your side.
Initiative is also now determined by different skills based on what you are doing - eg. if you are sneaking, you would roll stealth instead of Perception. this implies that the actions you were up to prior to entering hostilities in many ways dictates how you will respond (and how fast you will react), once initiative is called.
the GM also has the ability to apply bonuses to Initiative based on the actions the PC's or Monsters are doing just before Initiative has been called.
per the CRB pg 468. "Rolling Initiative marks the start of an encounter. More often than not, you’ll roll initiative when you enter a battle."
so you DON'T want to enter battle until you want to enter battle. Surprise here is determining (when possible) when to start a fight. in the GM section, calling initiative is the transition from Exploration mode into encounter mode.
but the key KEY element is on pg 498 Rolling Initiative: "Call for initiative once a trap is triggered, as soon as two opposing groups come
into contact, or when a creature on one side decides to take action against the other."
holy crap, long winded way to get to my point

worth noting, save for one little side-bar on pg 499, there is no use of the word surprise anywhere for combat.
so, here's how my group has interpreted all of the above. Combat starts "as soon as 2 opposing groups..." or "when a creature on one side decides to take action..." the key here is to either not be perceived as an opposing group or to not force a decision to take an action until its on your terms. how is this done? entirely through your actions in Exploration mode prior to the start of combat.
Example 1: kick down the door, rush in. monsters automatically perceive you as an opposing group, initiative is rolled as soon as the door fly's open. you are at a (possible) positional disadvantage because you are at the door and will need to move a certain distance to get within striking range of your opposition. this costs you actions that could be otherwise allocated for other purposes.
Example 2: same door, you hear the monsters, some of the party sneak, and some are going to try and bluff their way into the room. door opens, monsters sense motive and seek - and discover something is amiss. at this point, same as example 1, you instantly transition into combat by calling initiative and PC's are at positional disadvantage.
Example 3. same as 2, but PC's pass all their exploration actions. monsters are completely oblivious. the sneaky sneaks are sneaking, and the deception of the pizza delivery is working. the PC's move into the room, they slide into position. Pizza Delivery folks get themselves into Flank position ahead of time, or close to the rooms BBG - whatever. Monsters are, like, "sure whatever, we love pizza!" and depending on what the PC's are doing, there may be other sense motive or seek what's going on. maybe not. until the PC's are ready. the PC's "spring the trap".
now, initiative is rolled exactly the same. Order is figured out exactly the same. 3-actions are exactly the same way, with the following differences. nobody gets a "surprise round". this doesn't exist
- if you were sneaking in exploration - you will likely roll stealth
- if you were pretending to be the pizza delivery dude - you might roll deception
- if you are hiding around the corner, waiting out of site for the "go" - you may roll Perception
- monsters, likely will roll perception
- GM, may decide that the pizza dudes get a +1 or +2 on their initiative because of role-play reasons. (optional)
now, you'll notice the flaw (if you think in a 5e mindset). rolling initiative as per normal, you or your side has no "guarantee" of going first. this is 100% correct. You better be using those stealth and deception skills that you are really good at to try and get into position (otherwise, you will likely have been caught earlier), but this is the vagaries of life and combat. there is no guarantee that the ambushing side will universally act faster. there is nothing to suggest that a monster may notice that slight twitch in your eye and they react quicker. the only thing you can hopefully do is decide when the fight will start, using the skills/abilities you have to give you the most advantage to try and go first - but once it starts, its all up to luck.
some may say this is not "Surprise" in the traditional sense. I 100% agree, but what I LOVE about this is the positional aspect of the lead-up to combat. if you can start a fight when you are flanking a foe, just due to the action economy, you have given yourself in the 1st round a huge advantage...
Anyway, that's how my table has interpreted things, and I honestly love it.
(now I'll grab some popcorn and wait to hear how stupid we are

cheers,
J.
couple quick notes:
- traditional "surprise" is described as 2 groups rounding a corner at the same time. Surprise! if lucky, your group can go first. this doesn't happen here. initiative, in a narrative sense, in this case determines which PC or Monster recovers from the surprise fastest and reacts first.
- note 2. I think of PF2 surprise as an ambush. nobody wants to setup an ambush and have the enemies spot it 100 yards away, they want the trap sprung in the kill zone. the advantage of an ambush is springing the trap in the kill zone, not individual reaction speed.