The United States is not the only country with nuclear weapons. The US President is not the only leader with a button to push.
Could? Possibly. If not today, then maybe tomorrow. There are plenty of movies that warn of such an event. In real life there has been at least (maybe more) where a nuclear launch was almost triggered due to an accident. For example: https://en.wikipedia.org/wiki/1983_Soviet_nuclear_false_alarm_incident
Is it likely? No. Am I worried in the slightest? Absolutely not. Why do I say this?
From my understanding, a nuclear war would destroy much of the planet Earth. In fact, so much would be destroyed that this would affect Bible prophecy. Nobody's going to saying, thinking, or believing in "Peace and Security" when they are digging all the major cities out of nuclear rubble while millions die from starvation, disease, and radiation exposure. Therefore, my faith has convinced me Jehovah would intervene if there was ever such a full scale war.
Does that mean nuclear weapons would never be used? No, it does not mean that. 2 such weapons have already been used in Japan 80+ years ago. Jehovah did not stop those bombs so we should be open to the possibility another such device could be used in the future. However, from everything I've read such use would need to be limited and it would depend on which group detonated such a bomb. A nuclear exchange between Russia and the United States would likely be full scale while India or Israel using the Bomb might be more limited and the likelihood of some rogue terrorist state having more than a single bomb is unlikely.