Kim knows that offense is best defense. US can not claim any victory and walk off, even with a stone claimed hitting NK key facilities to gain face, as long as NK proved no lost of offensive abilities, by counter attacking US targets in Japan or Kim-Chi-land.
Yet the BEST offensive is a sudden invasion to occupy Seoul after nuking US bases in e.g. Busan. Take at least 20 millions Kim-Chi cousins as hostage / human shield to cover nuke troops and Kim Command Center. That will be a most stable long term solution and good point of balance.
Gaining such advantage, Kim can nuke Washington, and US can not hit back.
Aka new world order.
Regardlessly, there is a Total Lack of any factor of Victory for USA, that it has any chance to reset it own setbacks in East Asia, extending any further time for it's badly weakened foothold there. Where they are currently trapped like an injured bear which foot is clamped and hurt in a bear trap.
Bleeding and screaming.
The future is absolutely sure that the US will lose it's status and interest, and military foot hold to China and Russia, one after another, starting from Korean Peninsula where it's doorstep of Russian Fareast and PRC.
NK Kim is a bait in this bear trap.
Any prolonged struggling US made here is going to cause it's limb lost in this trap. If the conflict here reached any higher levels, only escalate the time for US to finalize it losses as the Ex-Superpower, and disintegrate like ex-Soviet.