Shielding sounds like exactly what you’re wanting to use. We use it in CDMS for the same kind of background studies.
You should note that Geant4 is not going to model “natural materials” out of the box. If you set your source, for example, to U-238, then on each event you’re going to get one decay from each step in the full decay chain, all the way down to Pb-208, with time stamps of millions to billions of years.
What you’ll want to do is (a) solve the Bateman equations to determine the secular equilibrium mix of decay-chain isotopes, given a specified age for your rock; and (b) write a custom generator (GPS can do this via macro commands, I think!) where you pick an isotope randomly from that secular mix. For a nice long run, you’ll get integrated results that reflect the natural rock.
If you’re only interested in gammas, there are packages like SOURCES4C (if you only care about gammas) or RadSrc from LLNL which can do this for you and give you a spectrum you can feed to Geant4 (GPS).