Here's an analogy:
The Flight of Dragons, I believe the book is called. It's all about how dragons would be able to exist in accordance to legend. It goes so far as to explain how the very chemistry that would allow a creature like the dragon to exist would destroy any evidence of its existence after the creature died.
Essentially, it says the dragon is a natural Hindenburg. It would fly by producing hydrogen, in a process that would dissolve an area bone material developed for the purpose, through some biological process or another, maybe involving bacteria. The numerous flight sacks were supposedly responsible for its size. When it dies, not only would the body decompose, but the bacteria or what have you that dissolve the bone material would continue doing so, only after death the bone would not regrow.
Now, can you provide evidence disproving that? No. Can you say that, as a fact, dragons existed? Obviously not, as according to that hypothesis there would be no evidence.
Now, before anyone says anything about gods not dying, that's not the point. The point is that it is something that we cannot say is real. Dinosaurs are real, they just aren't alive anymore. As with dragons, which we cannot determine the reality of, we cannot determine if gods are real or fake. After that, it's all up to belief. You cannot say one is right or wrong. You cannot deny one or the other based on unlikelihood, because unlikely things happen all the time. At the same time, there are situations in which the unlikely chance does not happen.
You don't know how it would work, so you don't even know the likelihood. It could turn out being very likely there are gods, after twenty more years of general research, or it could turn out that twenty more years of research in general turn up evidence that suggests strongly (far more so than now; the tech of now is pathetic in this regard) that gods or God does not exist.
You cannot say as a fact that there is nothing to believe in, neither can you state as a fact that there is something to believe in.