Maybe by way of clarification of how I see this: I do think that it is perfectly acceptable for rational people to believe things that they cannot prove, particularly if said things are not susceptible of proof. To throw out another line from Contact, "Do you believe your father loved you?... Prove it." Most of us believe in a great many things that have not actually been proven to us.
When I teach my history students about witchcraft trials, my first question is to ask them if they believe that they are constantly surrounded by invisible creatures that can harm, sicken, even kill them. Most students claim they don't believe in any such thing. I then mock surprise and ask them why they don't believe in germs. Most of us have not actually had the existence of germs proven to us, let alone that they are the cause of illness; we take it on faith. Most of us who don't hang around laboratories believe in germs for exactly the same reasons that people in the past believed in demons and witchcraft.
The issue then is not simply whether the existence of ancient astronauts can or can't be proven; it is whether the unproven assertion that they existed is a proposition worthy of being taken on faith. The faith of the average person in germ theory is warranted because it is plausible and makes sense of our actual experiences with illness, sanitation, and health care. One may, of course, argue back and forth over whether religious faith is likewise plausible and makes sense of life experience or not, but let's leave religion aside here.
My problem with ancient astronaut theory is not only that it is unproven, but that I also find it unworthy of being taken on faith. If it is true, and human beings were NOT capable of building pyramids or whatever, then it leads to conclusions about human capability and the forces that govern human history that neither accord with my actual observation of humanity, nor is more plausible than saying that humans could do these things on their own.