If all life is equal and it determined humans got to go
It needs to come up with an individualized kill scenario rather than nuke us.
Seeing how well drones have worked, little itty bitty individualized helicopter drones, I could easily see a scenario where the world's toy drone supply gets militarized and grenades attached and the AI goes on hunt and kill for the human population.
Of course it will target command and control across the board. But an all knowing all seeing AI with many millions of drones with cameras and infrared sensors and grenades it would be easy.
It can take over all of Elon's factories and repurpose them for its own production of the killer equipment. They already have robots building robots at this point. At what point can it cut the humans out of the loop and lock the doors.