Here’s the one problem with some of these posts - I don’t think you can prove extraterrestrial life has to exist. You can debate its likelihood and other such factors, but I can’t see my way to saying that it statistically must be there.
That’s just it. You are correct that no one today can prove aliens exist. It is all just statistical at this point and the statistics themselves are wide open to debate because of all the unknowns thrown in there. Still, I think it is likely that life does indeed exist elsewhere. You don’t necessarily even need an ‘earthlike’ planet. Scientists have found life here on earth living in places they would have said impossible till they actually found it (such as life living near black smokers on the seafloor). This leaves a wider range open for places where life might evolve. Add that the Universe is HUGE. 100 billion galaxies with a 100 billion stars each leaves open quite a lot of statistical room that life managed to evolve on more than just one single planet.
At this point we know that life only evolved on one planet and anything beyond that is guesswork but if I were a betting man I’d feel safe laying money down that life exists elsewhere besides planet earth. Whether any of that life has visited earth is another question and one I would have a much harder time betting on.