The claim that a statement is true because one cannot imagine (what one believes to be) the necessary precondition of it being false to be in effect. That can fail in one of two ways; the preconditions may not be necessary, and the conditions may be in effect even if the claimer can't imagine how it could possibly be so. Often it takes the form of a claim that something has been proved to be false/true because it has not been proved to be true/false. Famously refuted by Carl Sagan with the statement, "Absence of evidence is not evidence of absence." Based on shifting the burden of proof onto whichever side of the argument you want to lose. If something can not be proven either way, just act like the opinion opposite of yours is inherently sillier, and you can assert that your position must be assumed correct until someone from the other side can prove you wrong. Usually involves an appeal to one's own authority and/or Burden of Proof Fallacy, and is essentially a claim of personal omniscience; if the arguer cannot imagine a way for something to have happened, it is clearly impossible.
The popular argument "you cannot prove X does not exist, so it does" (or vice-versa) is the typical case. X can be God, aliens, a huge government conspiracy, unicorns, whatever. It's more common with arguments that are harder to prove, one way or the other.
In the Chick TractBig Daddy, the protagonist invokes the God Of Gaps (see Bill O'Reilly below for details) claiming that since we don't know what holds protons and neutrons together, it must be Jesus note At the time the book was published, the gluon was not proven, but was a widely accepted theory for ten years.
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Bill O'Reilly's infamous tide argument, which basically boils down to "I don't understand how tides work, therefore they are completely inexplicable and God exists." The O'Reilly logic proceeds as follows: 1. I'm the smartest living thing ever to grace the Earth with the imprint of his foot, therefore no one else understands anything that I don't. 2. I don't understand what causes tides. 3. Therefore no one else understands what causes tides either. 4. There is no possible explanation for the tides except.... 5. God gone done it! Thank you Jesus for giving us the miracle of tides! 6. Witches burn because they are made of wood. 7. We can test for witches by seeing if they float on water.
O'Reilly's lunar argument above is simply a variation of another version of this trope: the God of the Gaps argument. It basically boils down to: "We don't know how 'Thing X' got here or how it works, therefore God, Q. E. D." For instance, if one asks "how does the sun orbit the earth", and the atheist does not know...on and on and on. Of course, one day there will likely be no more gaps for God to populate, and the argument is logically untenable even if there were. This argument was first identified and comprehensively disproved by Dietrich Bonhoeffer, a Christian theologian later executed by the Nazis, who pointed out that even if there is a gap in mankind's knowledge, the theist who says that "oh, so it must have been God" has no logical or factual basis for that decision. This is also a favorite of creationists to deny the effect of evolution, as a lead-in to claiming creationism is then the default alternative. "I can't imagine the preconditions necessary for it to be possible for inanimate matter to turn into life possibly being true, therefore those preconditions aren't valid, therefore life didn't form on its own from inanimate matter, and god did it instead. And in the process he made a garden. With a tree and a forbidden fruit, and a talking snake, and he made the first man out of mud and the first woman out of his rib. Because that's the default alternative."
The 'Devil's Proof' was a favorite of Battler's early in Umineko: When They Cry. Until Knox's 8th was declared, Beatrice had to knock these down individually, though she once used Hempel's Raven to turn the burden of proof back to Battler eighteen-fold.
The Bielefeld Conspiracy is a satirical example. Asking a random person "Do you know anybody from Bielefeld? Have you ever been to Bielefeld? Do you know anybody who has ever been to Bielefeld?" is highly likely to garner three "no"snote Bielefeld is a mid-size town in North Rhine-Westphalia, Germany, with no particular thing to attract attention to it and no particular dialect that's really distinguishable from Standard German, so it is "concluded" that the city does not exist.