Avoiding the paradox
I think that the minimum belief that people must have before searching is that there is something there for which to search (or at least a belief in a reasonable possibility of success). Otherwise, why would anybody search?
Searching to disprove the existence of alien intelligences isn't sufficient motivation, and invites suspicion that the search wasn't rigorous or complete; not to mention the logical difficulties that come with trying to prove a negative. Only people who want to find something can be believed when they fail.