One solution to the Fermi paradox is that there is no paradox. We don't know what to look for, and we've barely started.
To reinforce this point: a metagenomics project has just discovered 662 new species of bacteria. From human navels.
It's a little arrogant to think that we've done all the looking we need to in order to say there are no aliens. Imagine pre-contact Native Americans spending an afternoon staring out over the Atlantic and at sunset saying, "Alright guys, enough of that. There's nothing out there."