It is a little simpler to locate and pinpoint a liquid-fueled rocket launch, given that much activity associated with the launch takes place prior to ignition, and this increased activity may be seen through surveillance techniques.
Solid fuel rockets are supposed to be much more quickly launched, with a minimum of other activity prior to actual ignition. But there is still activity of actually moving the missile into position, and though the warning period is much shorter, it is still finite.
But until the launch is rising from the pad, its direction still cannot be determined before it has begun its climb, at which point the probable paths become known, and with the high degree of sophisticated coordination of the tracking technology and the launch of a counter-missile, the kill approaches the inevitable.
And of course, given the successes the North Koreans have had in many of their attempts, a good many of them simply blow up on the launch. For all their supposed sophistication, they are still a Third World country or maybe even worse. And they do NOT have infinite resources.
Israel shoots down missiles regularly. It works.