HENRI: Post-trans-uranic alloys require enormous energy to create. The most efficient generators, annie plants, require PTU's in their construction, presenting a bootstrap problem.
It takes thousands of years for technological societies to build their first annie-plants, unless they get a leg up with a loaner, like we did.
Now, if every annie plant in Sol system was immediately devoted to doing nothing but spinning out PTU's for construction, we could build something like this shortly before our sun dies.
Or maybe shortly after. My simulation's still kind of iffy on that last quarter-billion years.