For ICBM test warheads they have a system that replaces the nuclear pit with a sensor package that measures the incoming shockfront, does signal processing and gets out a radio signal before the entire thing is crushed.
So if folks truly cared, it's possible to design a computer system to boot up, in a barebones fashion, and then do meaningful work and then transmit it, in under a millisecond?
Certainly, and I imagine that there are plenty that we interact with on a regular basis. For example, door security sensors (like for Ring) will be off nearly all the time. When someone opens the door, they will power up, send a notification, and go dormant again. I don't know if this will happen within a single millisecond, but it certainly could if there was a design need.
For many simple embedded systems that plug into the wall, the "boot" process will happen in under a millisecond. But it will take considerably longer than that for the voltage levels to stabilize.
The real thing which differentiates these from a PC or phone is that they are not running what we would typically call an OS. They may be running an RTOS (a very simplified OS), but for many of them, as soon as they have stable power, they are off to the races (Just like the home-computers of the 80s. Just plug in and go.)
Because I understand electronics just enough to know that sending a usable signal in under a millisecond from cold is incredibly tough. That's barely enough time for voltages to stabilize in even quite high end systems.
Like I said link a microcontroller that can meet that. 'Usable work' can be as little as adding two half-precision floating point numbers together, and sending it can be any possible method.
