>>12100406You've never read the books, have you?
The Pak Protectors devised a method of cheap mass transmutation of matter to create the 'scrith' the foundations of the Ringworld is made of. To get all the material they needed, they converted all planetary bodies, asteroids, comets, and whatever else they could get their hands on; in any case they needed to clear out the entire system anyway to make room for the Ringworld itself, you wouldn't want the gravitational sources around nor large planetary bodies to crash into it.
So if you had the means to build such a structure in the Sol system, you'd have to do the same: clear out the entire Sol system, converting it to your super-strong Ringworld foundation material.
Sol of course has to be at the center, 193M miles away, to give an Earth-like solar exposure. You set your Shadow Squares rotating to give you 24-hour 'days' on the inner surface.
All in all shouldn't take you more than a few tens of thousands of years for the project. xD