If something can only be proven to a 99.999999% certainty, is that still "unscientific"? What if scientists predict something happening with only 0.1% chance, for example the likelihood of a particular asteroid hitting earth? Or what about 60%, like a typical weather report predicting rain.
Generally, the high, low, or intermediate likelihood of some event happening does not make it unscientific.
While it would be unscientific to simply say that aliens exist, it's plenty scientific to consider the rate of star formation and age, conditions for life around stars, and time it takes to develop intelligent life to say that there is a particular likelihood of there being alien life.
Like I said in another comment below - you're assuming information is distributed uniformly across the universe, which we don't really know and can't assume because it certainly isn't in the solar system.
> what exists or doesn't exist in the universe that's not visible is pure unscientific speculation
I don't see anyone saying that the existence of aliens aren't speculation or that "aliens exists" (or your: "aliens don't exist") isn't just a personal belief as stupid to argue about as religion. But as countless wars have shown, people (like you) will try to create conflict from differing personal beliefs. Just because you drop "Occam's razor" doesn't make your belief the correct one.
The singularity was infinite. Space is infinity, but bigger.
Everything you said is unsupportable
What's out there outside the observable universe is fun to speculate about, but it's armchair philosophy, not science. Maybe there's an infinite variety of life and somewhere out there right now Gandalf is wielding a light saber while riding a dinosaur. Maybe we're alone in the universe because the Earth so happens to sit right on the only information complexity singularity in the universe. (We really don't know anything about the information structure of the universe yet; all the "dude, the universe is really big" arguments assume that information is distributed uniformly across the universe, but this obviously doesn't match observed reality.)
Of course what exists or doesn't exist in the universe that's not visible is pure unscientific speculation; might as well be made of blue cheese as far as science is concerned.
> Space is ridiculously big. The universe is ridiculously old.
This isn't true. Mathematical concepts of infinities and limits are "ridiculously big". Space is finite and thus ridiculously small.