CatBus, the problem with your imaginary duck hypothetical is that it relates to nothing. If theists viewed God in that way it would be just as nonsensical.
The duck was a man-made invention that was purpose-built to be an entity that can neither be disproven nor fully understood. So in that sense it’s exactly like gods – the fact that theists and atheists view such things differently was the point. The feathers were added to highlight the implausibility angle.
Sure, atheists view things differently, but the kind of duck deity you conceptualize is wholly unlike God conceived by most theists.
That something can’t be disproven or fully understand doesn’t mean it doesn’t exist. Science proceeds on all manner of theories that can’t be disproven.
Two books come to mind which I can’t distill very well without more time and thought. First, in “Reality and Identity” by Emile Meyerson (available as scanned on archive.org), there is a good exploration of provability and questions about the foundations of scientific understanding. If you’re super interested/motivated, pages 27-28 get to what I have in mind.
In passing, free will is mentioned. Free will is a concept that seems the go-to junction of science and religion. So far there is no resolution of the question whether free will exists.
Which brings me to the second book, “The Measure of Man,” by Joseph Wood Krutch. The gist is similar to the aforementioned pages by Meyerson, but focused on free will. Basically, whatever science might possibly explain, it can’t foreclose the existence of free will, though science tries. For Krutch’s purposes the existence of a God is neither here nor there.
Maybe free will is like an imaginary invisible duck, but I don’t think so.
I see the same relation in those debates to the debate over whether God exists. And if free will exists, we might ask pesky questions like where does it come from.