I think many involved in science want there not to be a God so bad, they go to almost any lengths to find a way to convince themselves he doesn't exist.
That's not how scientists think, but that IS how creationists think. They want their deity to exist so badly that they go to any lengths to convince themselves that the contradictory evidence doesn't exist. I think you're projecting.
That's one of the reasons I have a problem with evolution. If it was really true that evolution is the way different species came to be, then there shouldn't be such gaps in the fossil records. There should be smooth transition. There should be more intermediate/transitional forms between different species. It should be the norm.
You're not qualified to determine what gaps are too large or how large they should be. Neither am I. We would have to know how likely it is for any given creature to become a fossil, what fraction of fossils have survived to the present, and what fraction of those are found.
You can't prove that. It's only speculation.
Even were that the case, why is that a problem for a creationist? That's the currency of a creationist's belief - speculation. He believes things that he can't demonstrate. Your previous comment about the size of the gaps in the fossil record was just speculation. And this is a good illustration of what I just said about creationists going to any lengths to deny the science, including introducing a double standard for religious and scientific belief. That cannot be justified.
Regarding your use of the word
prove, you've probably been told that little is proven in science. The standard is demonstration beyond reasonable doubt, which has been done. The theory is correct beyond reasonable doubt. Those rejecting it don't have valid (properly reasoned) arguments. Their doubt is unrelated to reason, thus not a reasonable doubt. They are unreasonable doubts.
As an exercise, think about what would become the new paradigm if the theory were falsified and how unreasonable it would be to believe that that was the case before falsifying the theory. You've still got to explain all of the evidence that we would then know didn't get there by blind forces of nature.
Let me give you a hint with an analogy. Suppose that we have mountains of evidence that a certain suspect was guilty of a particular murder - DNA, fingerprints, eyewitness accounts, closed circuit TV, ballistics, etc.. all pointing to the same suspect, who was convicted. Then one day, something is uncovered that falsifies the verdict, whatever that might be, and we now know that the theory of the murder was wrong. What's the new paradigm? It's fraud. Somebody went to great pains to deceive, perhaps the police, perhaps enemies of the suspect.
So what do you suppose the new paradigm would become? Biblical creationism? That's ruled out by the existing evidence, which would now need to be reinterpreted in the light of the falsifying find, but that doesn't resuscitate biblical creationism. It would, however resuscitate creationism by a deceptive creator or creators (fraud again), but not the kind humanity could have perpetrated, as some of that evidence is in the DNA and some fossil evidence will eventually be found as the ice caps melt away. Man couldn't have engineered either of those.
So who did? The default paradigm would be that the earth had been visited by a race of superhuman extraterrestrials that themselves arose through naturalistic processes (abiogenesis and evolution) orchestrated a massive fraud, or a supernatural explanation with supernatural deceivers. The latter would still be an unreasonable doubt given the absence of evidence for supernaturalism and the lack of need to invoke it over a naturalistic hypothesis, which though presently also unreasonable to believe, would become the leading hypothesis if the theory were falsified.
I must also say that question about leprechauns is ridiculous
Not to an atheist or even an enlightened theist who understands that the evidence doesn't support his beliefs but chooses to hold them any way presumably because it's comforting or familiar.
This is an interesting phenomenon to me - the believer who is offended by having his deity compared to other things believed in by faith. It's predictable that some theists would feel this way to anybody that can imagine what it's like to be a zealous one.
And should the atheist be offended that you call this analogy ridiculous? I doubt any are. Can you not see how the world looks to him the way he can see how it looks to you? Are you unable to see how a leprechaun and a god are equivalent to an atheist, assuming that he is also an aleprechaunist, and that he is not trying to offend you?
What other insufficiently evidenced character that people have believed exists but which you don't believe in could the atheist compare your god to that wouldn't be ridiculous in your estimation? A ghost (assuming that you don't believe in their existence)? Another god, but one that you reject, like Zeus or Odin? Whatever the answer, substitute that for leprechaun.