The Fermi Paradox, of course, is a paradox. DNA in the stratosphere is halfway a joke, but other interesting ideas which I don't think we're quite technologically capable of yet include looking for green light reflecting from the surface of an Earth-size planet in the Goldilocks Zone, or (I love this one) bright light coming from the night side of the same.
My own thoughts on why the Aliens haven't visited us are that FTL travel actually doesn't exist and the energy expenditure to send a crewed vehicle across light years really is too much.
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