Aside from we don't know even in theory how to do it, which is a bit of an obstacle to overcome, I don't see how this could work without developing AGI first to operate it. That's probably at least a couple of trillion worth of R&D right there, and then again we don't actually know how to start on that even in theory.

In total the US already spends half a trillion on R&D per year. The US military spends a trillion on R&D every 15 years and the IT industry does about the same, and bear in mind most of the research these organisations are already doing would be directly relevant to a project like this. So in a way we're already doing it, and I don't see any from-scratch full-civilization self replicating technology architectures coming along on the horizon even as a theoretical exercise. Even for something like interstellar probes at least we have outline designs.