Good question. The CBO expects it to cost $800 billion, the white house says $175 billion.
Practically speaking, America already has
an advanced ICBM defense system, although as currently deployed, it is aimed at stopping missiles from a rogue state (specifically North Korea).
In the end, the Golden Dome might just end up buying a bunch of ground-based THAAD interceptor missiles (which are already in production), along with some space-based detector satellites. The sooner you can stop a missile, the cheaper it is because MIRV (multiple-independent-reentry-vehicle) ICBMS are very expensive to stop once they've split, because there are a lot of them and they are moving fast (along the order of mach 25). So if you can stop them earlier in flight it's cheaper. Estimate roughly $1 billion dollars spent to stop an ICBM in the terminal phase, so stopping a full launch of nuclear missiles by Russia would cost trillions of dollars.
The controversial part of Golden Dome is putting interceptors in space, since that is weaponizing outer space. That also concerns me, but we might not actually get there. The idea of ICBM interceptors is controversial to some people, but those people don't realize it already exists, and is deployed.