Aliens will be discovered first. Just going by the Drake Equation. But in even more simplistic terms, let's just say the chance of life, like on Earth, is 1/10,000,000,000. Impossibly small, right? Almost statistically insignificant. Well, we know that there's are 10s of billions of stars, many of which that have Earth like planets within the star's habitable zone, in the Milky Way (our galaxy) alone! So even in our own galaxy, it's possible to have at least 10 other planets that can sustain life (and that's on the extremely low end). Now imagine that on the scale of the observable universe. That number of planets that can sustain life goes up by many orders in magnitude. Now imagine that on the scale of the unobservable universe. Planets capable of life may be, for all intents and purposes, infinite (unless there's an end" to the universe).
Bigfoot? Conspiracy theory about a "missing link" but we have 0 evidence for it and more importantly, no way a terrestrial creature that is supposed to be similar to humans and apes can remain so elusive and rare, yet sustain a population.
Ghosts? A manifestation of the consciousness of people who are dead? We know our consciousness comes from the brain, and the brain doesn't "pass on" when it dies. It degrades, just like the rest of your body. So when you die, your consciousness dies as well. We have no reason to believe that consciousness can exist without a brain.
God? Which one? The Abrahamic one which no one may look upon his face and live [Exodus 33:20] (even though Jacob looked at him face to face and lived Genesis 32:30)? Well, there will be no discovering him because we'll supposedly die and won't be able to bring evidence back to believe he was discovered. And he's supposed to be invisible anyway, so we can't really "discover" him. Couple that with the fact that he's not real (just like ghosts and bigfoot) and it's a no brainer that he won't be discovered. What about Zeus? Well, Mt. Olympus has been climbed and welp...no Olympians.
We at least have reason to believe aliens are out there because we know life is possible in this universe. And even if the conditions for life need to be similar to Earth's (amount of oxygen in the atmosphere, planet size because gravity matters, air pressure, etc) we've already discovered several planets that meet that criteria. And we have reason to believe that the condition's don't need to be like Earth's. When we think "life", we think carbon based, DNA to give it's characteristics, and oxygen to breathe. But we've discovered organisms that are sulfur and arsenic based, so the "conditions for life" in lay terminology isn't even necessary for life in other places. With that known, the amount of Earth like planets doesn't even matter, unless we are looking for aliens that are like us or our animals.
