The Fermi paradox points out a contradiction between our expectations and evidence. We believe that extra terrestrial life is likely to exist, and therefore likely to have visited earth–and yet there is no evidence that it has. What I’m going to suggest is that there is a very good reason we wouldn’t know about it, even if it did happen. The solution I’m going to suggest is not yet listed among the explanations on Wikipedia as far as I can see.
Earth has been around 5 billion years. Humans have only been around a few thousand. My belief is that if extra terrestrials did visit and found intelligent life, it would be interesting enough that they would come back around frequently to check in on us.
But what is frequently? If space travel is limited to sublight speeds, then visits are extremely expensive. That may mean one visit every few hundred years at most. If visits are truly that rare, then the most recent visit may have been in the 1600’s or so, and we would not be able to properly vet or verify the incident and it could not be treated with scientific credibility.
If there is no intelligent life, landing on earth may be less of a priority and return visits might be less frequent. Probes and landers would likely be sent to where the highest concentrations of life occur: in rain forests. Rain forests will tend to destroy or consume any artifact exposed to them and make it even more difficult for us to determine whether we have been visited.
If we assume, however, that extra terrestrials exist, and estimates of intelligent life in the universe are correct, then our first contact may happen soon (if you assume, as I do, that they would not hide from us), during a regularly scheduled 300 year checkin. The Jews have kept a place setting for the expected Messiah for a few thousand years. I plan to put out a plate of live gagh and blood wine once a year. 😉