Evidently you’ve never seen a government operation at work.
A trillion dollars is a very low estimate; it’s be a miraculous achievement to put a large permanent base on the Moon that cheaply. What you’re proposing is the creation of a space launch capability on a scale unprecedented in the history of spaceflight. All the money that has ever been spent on space exploration in the entire history of aviation did less in space than you’re proposing.
If you could put a base on the Moon for $20 billion it would have been done by rich guys by now.
I’m still a bit confused as to why this would be a better idea than nuclear weapons, which are cheaper and don’t require going to the Moon. Radiation? Drop a multimegaton rock on the Earth and I assure you you’ll have a lot of concerns besides radiation.
Even if this was possible, which it isn’t, you simply couldn’t get it up and working BEFORE it was nuked. Do you really think the world’s other powers wouldn’t notice you were building a gigantic rock gun on the Moon, and wouldn’t vaporize it?