Let’s grant for the moment that somehow, the fully functional and the irreducibly complex genetic code necessary for a single eukaryotic, or even prokaryotic cell, came into existence by happenstance (or by panspermia, perhaps, or by an infinite number of parallel universes — pick your deus ex machina mechanism). Even with a “cheat” like this, could the evolutionary process take it from there?
Spontaneous genetic point mutations, in which one of the four DNA base pairs is swapped for another, do occur from time to time, at a rate of around 1.1×10−8 (https://academic.oup.com/genetics/article/156/1/297/6051861?login=false) per base pair per generation (that’s one in 100 million). However the vast majority of these are either negative or neutral. They’re typically neutral if they occur in the non-coding segment of DNA, which is not used as blueprints for proteins. (We’re still not entirely sure what the purpose is of all this non-coding DNA. There was a time when all of it was thought to be “junk,” or leftovers from previous evolutionary steps. Now we know that at least some of it serves a purpose: of regulation, saying when a given sequence should or shouldn’t be transcribed, where the coding gene begins and ends, binding sites for the transcription mechanism to begin, kind of like the coupling component of a zipper, and things like that. Telomeres, the caps on our chromosomes now known to be one of the determining factors of biological age, are also part of non-coding DNA. Other segments of it protect the structure of the chromosomes so that they maintain their integrity during cell replication. No doubt more purposes will be understood in time, but I seriously doubt any of it will turn out to be “junk”).
Negative DNA mutations in coding sequences is one of the mechanisms by which cancer occurs. These can be either “nonsense” or “missense” mutations. Nonsense mutations are when a point mutation forms what’s called a “stop” codon (where a codon is a set of three base pairs, forming a “word” of sorts.) Rather that continuing to code for a protein, the stop codon in the middle of the sequence would simply prematurely truncate the protein code entirely. Missense mutations occur when a point mutation switches one codon to another… like turning “cat” into “bat” or “rat,” with an entirely different meaning. Each codon calls for a different amino acid, so such a mutation may substitute a different one with different chemical properties, which (if those properties are different enough) might contribute to different stereochemistry, or folding of that protein once made. The stereochemistry largely determines the protein’s function, so it might be thus altered (and nearly always for the worse)… though there are are redundancies, such that multiple codons call for the same amino acids (there are only twenty amino acids, after all). So it’s possible the mutation might be “silent” even if in a coding sequence of DNA, in this case.
Environmental factors known to increase DNA mutation rates include things like ionizing radiation (UV, x-ray, gamma ray, etc), and various carcinogenic chemicals. If these mutations occur in germ cells, they can be passed on to progeny, assuming that the mutation isn’t rapidly fatal before it can be passed on. In some cases, the resulting “disease” may confer a survival advantage in a given environment–for example, sickle cell anemia, a point mutation that changes the shape of red blood cells. It does indeed cause severe disease, but it also happens to protect against malaria, endemic in Africa. This is probably why sickle cell is far more common in Africa that in other parts of the world.
But it’s quite a stretch to say that was a “positive” mutation. Sickle cell anemia manifests with recurrent hemolytic crises, in which red blood cells burst, leading to severe low levels in the bloodstream (which means not enough oxygen for the tissues). Red blood cells can also get stuck in small vessels, leading to clots, spleen and liver enlargement, etc. Sure, the mutation happens to have a survival benefit in Africa, but “positive,” the way a sudden functioning eye might be? I don’t think so.
And that’s the thing: we can’t point to a single known unequivocally positive DNA mutation. The most we can do is identify some “bad” ones that happen to have a silver lining in a particular environment. From there, evolutionists extrapolate (tremendously!) that in the distant past, many such mutations must have occurred–even though we have no evidence that they did, and all evidence we do have seems to suggest otherwise.
I’ve seen some sources that speculate that positive mutations occur about 1/1000 times per generation, though the paper, “The population genetics of mutations: good, bad, and indifferent” (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2871823/) makes the point that this is an exceedingly difficult number to quantify, because how one mutation might interact with another, let alone how multiple mutations might interact in a larger organism, is so very complex. Nevertheless, if we go with the 1/1000 number (which seems like as reasonable an estimate as any), since any sort of genetic mutation (a point mutation anyway) is supposed to occur only 1/100 million times per generation, that means a single positive mutation might occur 1/100 billion times per generation. Since earth is estimated to be 4.54 billion years old, and a generation is usually defined to be about 20 years, that’s 225 million generations since the dawn of earth’s time, by secular calculations.
Do you see the problem here? If those estimations are even in the ballpark, there hasn’t been enough time statistically for even one unequivocally positive mutation to occur. The universe literally doesn’t have enough time for evolution to occur (unless you introduce multiple universes… and even then, you’d need a near infinite number of them).