Any ballistic missile fired from the DPRK would be detected almost immediately by either US radar systems in South Korea, naval vessels in the Sea of Japan or satellites in orbit.

Once a weapon is detected, those systems will begin evaluating the trajectory of the missile which will help in determining the impact point. Depending on where that missile is headed, travel time would be in the neighborhood of 15–30 minutes.
20 minutes max. The launch will be detected within 5 minutes by Norad/American satellites. At least one, maybe more American nuclear subs hiding in the deep waters off the Korean peninsula will be ordered to move closer to the surface to initiate launch procedures for its 20 nuclear missiles – (each missile carrries mutiple nuclear warheads.)
The North Korean warhead detonates somewhere near Los Angelese, immediately killing or injuring several million in one of the most densely populated counties in America and creating a huge radioactive cloud of dust and smoke from massive wild fires that will rage like an inferno over Southern California.
5 minutes after launch, dozens of submarine launched American nuclear warheads begin raining down on military and civilian targets in North Korea destroying every city, and military base and killing half the residents of North Korea outright (the rest will die of starvation, burns, and radiation exposure as they desperately try flee to China or South Korea . . . the radioactive dust clouds drift southward towards parts of South Korea resulting in the deaths of hundreds of thousands, maybe millions of South Koreans.
This radioactive cloud will eventually be carried by the jetstream around the world. Of course none of that matters if China and Russia retaliate against the USA for hitting so close to their soil, because that’s the end of civilization as we know it.