The simplest and hence most likely solution to the Fermi Paradox is that we don't see evidence of advanced civilizations out there because there either aren't any, or they are exceedingly rare. Correct me if I'm wrong, but I don't believe Fermi even saw this as a paradox so much as proof that these civilizations were largely non existent in the vast majority of the Universe, and his statements on the matter were basically a response to people who felt differently.