In short, no.
There is absolutely no evidence that evolution, in the sense in which this question is referring to it, has ever happened.
Evidence of the lack of evidence includes the "theory" of Punctuated Equilibrium, developed by evolutionary paleontologists Niles Eldredge and Stephen Jay Gould. One of the celebrated functions of this theory is its demonstration of why, if evolution were actually true, there would be no fossil evidence for it. If evolutionists are wasting their time trying to explain why there is no fossil evidence for evolution, and why we should expect that there will be no fossil evidence for evolution, you can rest assured that there is no fossil evidence for evolution.
Since the Bible is the Word of God (2 Timothy 3:16), and it is impossible for God to lie (Hebrews 6:18), we know that, at minimum, God specially created mankind out of the dust of the earth (Genesis 2:7). So, with absolute certainty, we know that man did not evolve from a more primitive life form.
Further, if one were to believe in evolution, then to be consistent, one would have to expect that it would be entirely possible for one's next child to not be human. In fact, there would really be no reason to reject the reports of prestigious magazines like the National Enquirer, with their headlines like "Mongolian Woman Gives Birth to Three Headed Cow". This kind of reporting is completely consistent with evolutionary theory, yet it is universally rejected as unquestionably absurd based on the gathering of observable, empirical and measurable evidence, ie, the scientific method. We repeatedly observe that when a human woman gives birth to offspring, that offspring is human. This is what the scientific method truly tells us.
So we see that science itself not only does not point to evolution, but actually points away from it. As has been stated by one evangelical author, "most scientists believe in evolution because they believe that most scientists believe in evolution".
With such a demonstrably unscriptural, unscientific and thoroughly non-evidential theory like that of the superstitious secular humanist dogma of evolution, skepticism is, at minimum, wholly justified.
However, there is more to this question than simply "does evolution disprove the existence of God?"
Ultimately, the root of the question as it has been asked is what is commonly known as "The Problem of Evil". Rephrased, "Since bad things happen, doesn't that prove that a good God doesn't exist?"
Even though I am happy to demonstrate that evolution has not happened, I would never even begin to suggest that "bad things" don't happen. In fact, the Bible itself proclaims that they do (Genesis 6:5).
So what are we to do with this? How can there be a good God when people die of cancer? When tornadoes destroy entire cities? When it appears as though the weak are killed off by nature and only the strong survive?
In order for people dying of cancer to be found to be inconsistent with the nature of a good God, the person asking the question must first presuppose that there is such a thing as an an absolute measure of right and wrong. If there is no absolute right and wrong, then why would it be inconsistent for any imaginable God to allow, or even cause, people to die of cancer? If there is no absolute right and wrong, then there is nothing inherently wrong with causing people to die of cancer.
Since the question itself presupposes that there is something inherently and absolutely wrong with God causing someone to die of cancer, the person asking the question presupposes that there is an absolute moral governance. But of course, this is the same as presupposing that there is a good God.
So, presupposed in the question is the proof of its answer. There must be a good God if evil exists. Otherwise, there would be no measure by which to call it "evil".