Why do atheists claim that the concept of God is so unlikely

[Mister Agenda]

Hello, I am hoping someone can explain the atheist viewpoint to me on the validity and probability of God's existence.

Atheists don't believe any God is real or any gods are real. Their estimate of the probability that one of them might be real depends on the atheist. Done and done.

Most atheists will claim that the facts show the concept of a God to be so utterly unlikely as to be considered impossible.

Well, the concept of God certainly exists, it's whether that concept corresponds to reality that's in doubt. In my experience, most atheists consider God improbable rather than impossible. Where do you get your numbers?

But, this is not what the facts show at all.

I certainly hope this is going to be convincing. If God is real, I definitely want to know.

The theory of Evolution does not explain the origin of life, nor can it explain the existence of life from the first organic cell onward.

Evolution is the theory that explains diversity and speciation. You don't expect the Germ Theory of Disease to explain gravity, do you? It explains exactly what it purports to explain. I am disappoint.

How does natural selection explain the eye, for example? How can atheists claim that complex organs like the eye could have evolved, when everything we know about the eye says that it is useless unless all the components are in place at the same time.

It explains it very well, and since the eye has evolved independently many times, we have splendid examples of eyes in every stage of development, from the eye spots of a tapeworm to the eyes of an eagle. I am sure there are videos that can walk you through eye evolution if you actually want to know. Or you could read the Wikipedia article or take a class. The information is readily available.

As for reptile-mammal transition evidence, where is it in "evidence"?

You picked another good one there, since the fossil evidence for the transition from reptile to mammal is abundant, including details of how what was part of the jaw bone in reptiles is part of the inner ear of mammals. And we have a few types of mammal that still lay eggs to accentuate the point.

What are the actual mechanics that achieve it? Not speculation, actual. Not variation in a genus [which evolutionists cling to as being evolution].

Psst. Variation within a genus that is conserved by natural selection totally counts as evolution, and in fact is a necessary part of evolution. You can't have change at the class level that doesn't start at the species level.

Biological changes where a living entity can be observed to be changing into something different, breaching the barriers of its DNA.

What barriers of its DNA? There's a Nobel waiting for anyone who can demonstrate a mechanism in DNA that would prevent an organism from evolving indefinitely.

For reptiles to become mammals, that breach must have happened. So, someone please show where reptiles are in a state of doing so today - where that transition is taking place.

There's no reproductive profit in trying to occupy a niche already full to brimming over, though something of the sort might happen somewhere where mammals are scarce. Now, if you're looking for examples of reptiles that give live birth (like boa constrictors), or are able to warm themselves internally (tegu), you can be obliged. One of them may eventually have descendants that would be considered a different class from reptilia; but they won't be mammals, they'll be their own thing, but they may resemble mammals in some ways.

The facts show that what is overwhelmingly in evidence is what the Bible itself says, that like begets like, and we  all rely on that to occur in all facets of life, from growing/eating fruit and vegetables through to human/animal procreation.

Your facts have all fallen flat. But like does beget like, if a dog ever gave birth to a cat on its own, that would upend evolution. The offspring are always the same species as the parents, except in certain cases involving hybridization. But some the descendants of your dog thousands of generations later might not be dogs any more, and probably would have trouble interbreeding with dogs of your dog's generation even if they're still basically dogs.

It seems that the evidence supports the concept of God, rather than the atheistic claim that "God probably doesn't exist".

It seems the evidence you've brought resoundingly does not support God being real, although evolution probably plays a role in the origin of the concept. What you've offered is so easily dismantled that you're likely to be thought a Poe (an atheist pretending to be a theist to make theists look dumb).