I always assumed he would end up deploying a weapons system to space. Of course he would have to pretend to be doing something else while he builds up the capability to prevent others from becoming nervous. Something silly like colonizing Mars would work, especially if he really leans in to the eccentric billionaire trope.
The building of the infrastructure needs a red herring, the actual deployment need not be secret because by then it’s a done deed. Once deployed you’d want people to know, to avoid a Dr Strangelove situation. A veritable sword of Damocles.
Certainly not, but one wouldn't need to catch every satellite launch for space weapon- one or two would be enough evidence to go public and warrant further scrutiny. There are a number of extremely savvy amateur astronomers across the world that track suspected military launches and publish their findings:
https://sattrackcam.blogspot.com
