I'm running an encounter in Cyberpunk Red where the baddies are chainsawing a hole into an immobilized car to kill the driver, and our heroes have to rush in before the bad guys finish drilling!
How convenient of the baddies to be encountered in the right moment, just barely before they finish their task!
This seems to be a recurring issue when it comes to certain time-sensitive encounters. How can this phenomenon be justified?
Out-of game the justifiation is easy: we are here for exciting encounters, not to have the characters stumble upon the slaughtered remains of the victim too late, or one where it's easy going, the victim is in no danger to die anytime soon, if they help or not. That is your justification: because it is more fun that way.
So, the question is about how often the characters can arrive on scene just in the nick of time in-game, without straining our suspension of disbelief. And to be honest, it sometimes does strain suspension of belief.
However, this is no different from many other constructs around the characters. Why is a random group of characters embroiled in plots to save the world so often? Why are monsters conveniently so strong that you can defeat most of them, and there are ample warning signs if not? Why is the military or police not sending out a squad of soldiers to take care of the problems? We constantly suspend disbelief for the sake of adventure.
Secondly, there may also be a perception bias here, much like when you think all traffic lights jump to red just when you arrive. There are lots of situations in adventures where the characters do arrive late and have to deal with the fallout of something that happened earlier, or where there is nothing to do about something that happened earlier. They just do not register in the same way the nick-of-time encounters do in our awareness, because they do not stand out like that. And there are lots of situations that happen, after the characters have long left the scene. The characters just do not happen to be there and will never learn.
The encounters seem static and staged because, as described, they are static and staged. It feels like the NPCs are in stasis until the PCs turn because, well, they are.
So, don't do that.
Instead, prep a timeline of events that will happen if the PCs don't interfere. All that's needed is a basic understanding of the relevant NPCs' motivations, intentions, and capabilities.
For your example, the guys on the outside have some motivation to want the driver dead (this may need more elaboration ... or not), they intend to kill him, and their capabilities include a chainsaw. The guy on the inside has some motivation for not dying (probably a given for everyone), an intention to avoid the guys with the chainsaw, and the capability of whatever is inside the car.
What we see here is a moment on the timeline so let's back it up and consider the whole thing, appreciating that I have no idea how this fits into your adventure and no knowledge of the Cyberpunk Red system but it should give you the idea:
Now, you can write this in times, days, rounds, or whatever fits your needs/system.
Now, the PCs can intervene at any point in the timeline.
Now, however this plays out, it won't feel like the NPCs were waiting in the wings of the player's story - it feels like there is a whole dynamic world out there.
The NPCs can set up the scenario early, such as by EMPing the car, setting up a jammer, and then using a blowtorch to get into the car. This method is quiet and avoids attracting attention from gang members or corps or security firms or whoever would guard the car. Whoever hired you for the job presumably doesn't want it going loud, because a rival corp or gang might just decide to steal the goods.
The PCs then have a window of opportunity to rescue the driver. It might take fifteen minutes to blowtorch through the car's security systems. So long as they arrive during this time you can have the people getting into the car realize they are there and then escalate to the chainsaw and blasting their way in because they don't have time any more.
