I don’t see either as being dependent on the other. In other words, you can believe in God and not in extraterrestrial life. Many religious people do in fact hold that view. On the other hand, you can believe in extraterrestrial life and not believe in God. I know many people who hold that view.
So I don’t see a paradox at all. According to the Google dictionary, a paradox is “a seemingly absurd or self-contradictory statement or proposition that when investigated or explained may prove to be well founded or true.” I fail to see a contradiction that two different people can hold either view. It’s all theory.
In reality, we do not know for sure that life exists anywhere other than Earth because we have never found any evidence of life, although we continue the search. We have yet to find even a fossil of a microbe from space. However, the laws of mathematical probability suggest that with billions of planets in this galaxy and billions of other galaxies, it is likely that there is at least microbial life somewhere, if not something more advanced. We just haven’t the proof yet.
Similarly, except for subjective experiences, there is no proof that God exists either, although people believe that God exists. Maybe both exist. Maybe neither exists. I suppose it’s a question of faith in either view.