This whole "rolling initiative, but having zero stimuli to indicate combat has started" thing, sorta smacks to me of the same kind of playstyle where the DM "rolls dice behind a screen for no reason just to keep the players on their toes". Like the DM enjoys toying with the players as much as with their characters. Likes to watch them squirm a bit in confusion and maybe fear.
I dunno, I've been thinking this one over a lot, and the 'no reason' thing is really rare.
People are naturally aware of danger. If you've ever hiked in unfamiliar areas far from civilization, the reality hits you that you're all alone, and you get very very aware of every tiny noise. It soon gets pretty easy to tell when a rustling sound is coming from a breeze, or an animal in the underbrush.
I did paintball for a few years. It was easy to hear a newbie trying to ambush you. They would tense up when you came by, so you'd hear a familiar, tense rustling sound and you could pop them before they shot. Even with experienced players, if the underbrush was dense enough to hide them, adjusting their aim created noise. If they had to turn a significant arc to aim, that gave you enough information to drop and start blasting in that general direction. I know because that's how I always got shot even after I got pretty good - always by one of the same three ex-military guys.
So, I could see a character that has a Heroic level of alertness totally doing that and more.
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So, for the worst case: The PCs all blew their Perception rolls to see the ambushers, the Alert PC is not surprised, and rolls well enough to go first, then I tell them the believable stimulus that would have tipped them off. I keep it necessarily vague - they did blow Perception - but enough to know something is about to go down.
Let's say it's an invisible Rogue in the woods. "You have a sudden sinking feeling of danger, and hear the slight sound of leaves crunch nearby."
It's a spellcaster casting Hold Person from a window in town. "You see a bit of aggressively circular motion in a window two stories up to the right."
It's a spellcaster casting Fireball from a castle 100' away. "You glance over to see a candle flame sized dot of light suddenly appear in of the arrow slits to the left."
If the Alert PC blew their Perception by a lot, I try to make it more vague. If they blew it by only a little, I make it more specific.
This has a bunch of house-rule like thinking, so it's just an 'at my table' thing that works for us.
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The really super-rare scenarios, like an invisible, silenced Mind Flayer blasting away with psionics, I'm totally fine having that go down as the thing that happens before initiative, and then resolving everything from there. That situation should be VERY VERY rare, and all the dice rolls should scrupulously happen first. I also try to telegraph those in the plot, make it available via character knowledge, etc. so they don't feel screwed over.
If that ever does go down, if they don't say 'Oh, we knew what they were capable of, we should have seen this coming!' then I feel like I kinda blew it as a DM.