So I've been running this game for years, and I've always operated under the assumption that "surprise rounds," like you would find in Pathfinder or some other RPG, aren't a thing here. Whenever my players have set up an ambush or stealthily approached a group of baddies before a fight, I've given them a boost or two on their initiative checks as a reflection of their preparedness. As far as I know, this is the standard model for representing surprise attacks in EotE.

However, I'm reading through Friends Like These right now, and there is a passage on page 67 that says, "the sensor net set up by the Thalassians alerts the camp of the PCs' presence, making a surprise round impossible ."

This stuck out to me, because, well, what? Are surprise rounds a thing in this system, and I've never known it?

No. That's just putting a narrative fence in the way of the notion.

There are several threads discussing this. However, all three CRB's are silent on this topic.

The Perception skill mentions surprise, but not it's mechanical benefits.

The simplest way to handle it is whatever hiding skill the group is using to setup the ambush vs the perception or vigilance of the party. Failure means that the bad guys get to act as they've setup with no chance for the PCs to respond. Then roll initiative after that first "round" has completed and continue as normal. Success means the party cottons on to something hinky and both groups roll initiative as normal, but the PCs can't target what they can't see.

I've never really used surprise rounds but I have allowed one PC or NPC to get in an attack without the enemy noticing before rolling initiative. I've been a bit inconsistent in when I allow it but I believe I'm going to move to the more often suggested way of giving difficulty dice to initiative checks of the party that is being attacked from stealth.

For me, if a PC or NPC from any side rolled a Triumph, they'd be able to perform a maneuver before initiative starts as a whole.

I’ve only had this come up a few times but if my players enter an area where enemies are lying in wait and have stealthier I let them do an opposed perception roll and if they fail then I let thier opponents get off a round of attacks before initiative is rolled.

I would do the same for my players but they have never tried to sneak up on people for an attack.

The ambushers roll Cool with boost dice, the targets roll Vigilance with setbacks. Boom, there's your surprise round.

I played a few rounds where a hidden marksman was targeting the PCs. It became Ranged Heavy VS Vigilance for the first round or two. Until they got a good idea where he was and Perception checked him. I've also done Stealth vs Vigilance when the PCs were boating through a swamp and hidden enemies dropped down. In each case, Failure, Threat or Despair meant the enemy got a hit in. If the PCs were succesful they avoided negative consequences.

I just handle it on the initiative roll by assigning a difficulty. I use range for the base same as making a shot. That can be added to with subsequent Perception checks needed for those that 'failed' their initiative checks and are clueless to the shooter's location if a GM likes, and then add Boosts for every PC that did 'spot' the shooter and now they're all yelling and pointing, or just skip it and say it's good enough as long as one person 'succeeds' their initiative check. Gives PCs with the high Vigilance and Uncanny Reactions and Perception a chance to shine. It also streamlines the whole deal into one roll as opposed to a roll for initiative, opposed Perception/Stealth rolls etc.