I think there are still animals popping up that we never knew about, would it be fair to say they didn't exist because we couldn't prove they did, even if they were discovered later that afternoon? Of course, that seems like a slipperly slope, you could also say there was evidence for these lifeforms, (like a certain kind of foot print or spore) we just didn't realize it when we saw it on account of not knowing what it was suppose to mean, like how a man who hears a loud noise, notices a fire raging nearby and doesn't know what lightning is might think of any number of explanations for this sudden combustion... except for lightning, of course.
"Proof" and "belief" seem silly when you get right down to it, I think, but as long as the sun keeps rising every morning, (give or take a few hours in most of the world) one can be forgiven for thinking it'll rise tomorrow, too. Evidence for dawn tomorrow in this case would be the dawn of every day since the start of time, I think.
Is any of this making sense? I don't worry about disproving things because proving things in itself is a flawed premise, as far as I can tell. You may have noticed the indefinites in this post. I probably can't prove anything I've said, (even the Sun thing) observing the world, this is the only mindset that makes sense to me.