From a sample size of one you can infer that the sampled thing exists / is possible.
You can't infer anything from a sample size of one, or a sample size of zero. That's ungrounded speculation, not science.
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Call the Bayesian police...
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Right. Depends entirely on the priors. But that's like a tautology in some circles...
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Subtweeting Drake Equation?
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Extraterrestrial life, for example
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You can build 95% confidence interval by taking x ± 9.68 |x| https://stats.stackexchange.com/q/157582/35989
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Size or frequency?
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This is not exactly related but, what do you think of the Drake equation?
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And the way to avoid proof contrary to an agenda is to not allow proof.
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