Unless he dies suddenly or violently, I suspect Trump will survive his Presidency. And yes, even though he can initiate a nuclear war, I don't think he can do so all by himself. In every other case I know of, more than one human decision is required to launch nukes. He will not be in a room alone pushing a button, there will be aides and military officers surrounding him, they will probably also have keys or codes, and its unlikely they will cooperate in such an action just because he has a fit of rage. It will have to be after some provocation by a foreign power, and as part of some plan or strategy that has already been planned out ahead of time in detail.

Of course, its not impossible that he might initiate some non-nuclear action or strategy that will provoke an enemy to launch THEIR nukes. For example; "The Syrians are using poison gas in their attack on that rebel stronghold. I told them there would be consequences. Execute Plan 41: Launch a full conventional air and missile strike against the Russian naval base on the Mediterranean as a retaliation."

And of course, in the event of a melee that might erupt somewhere (like in the S China Sea) a sudden and unexpected event (like someone losing a capital ship) might trigger the other side launching the first nuke by accident. You can count on the second one being fired on purpose, no matter who does it. I am much more afraid of tactical nukes than I am of strategic ones. There are many more opportunities for something to go wrong.

Both the US and the Russians (and the Israelis) have accidentally shot down civilian airliners, (the Russians also shot one down on purpose!). If that can happen because of the decision of some trigger-happy local commander, then anything can happen. The only way a President could avoid that type of accident would be to make sure that type of situation is avoided in the first place. Trump doesn't strike me as the kind of person who thinks that far ahead, and he does strike me as the kind of person who will do anything to save face and avoid looking weak.