That's not how nuclear triggers work. There a multiple layers of safe guards. I would be more sympathetic to your position if you were to solve for the multiple layers of social engineering needed to fire a nuke. That is a more plausible path.
This is one of many examples of the general truth that if some entity or group is better at science and at long-range planning than people are, that entity or group is a threat to people.
Maybe it lies about a vaccines effectiveness. Maybe it’s not really a vaccine.
Maybe it cheats at an election and gets someone hired that will likely unknowingly help the ASI.
Maybe it strings together a thousand ideas that all look safe taken one by one, but cause effects that interact to cause massive problems.
You can’t imagine what it’s capable of. You simply aren’t smart enough. No one is.