Popular Science asked this very relevant question in its November 2010 issue. The answer is "probably". This is because "within around 10,000 years ago, people had lovely shoes", according to Will Harcourt-Smith, and expert on early-human fossils at the American Museum of Natural History in New York.
Beside Harcourt-Smith, PopSci also interviewed such renown authorities as Tim James, who specializes in fungi evolution at the University of Michigan. (Fungi supposedly evolved 1.5 billion years ago). James states that "the fungus that causes athlete's foot thrives in moist, unhygienic environments, which is why most people pick it up in locker rooms."
Also interviewed was Bob Neinast, the lead blogger for the Society of Barefoot Living. (Established in 1994, I bet you didn't know there was such a society). He helpfully adds, "it turns out that athlete's foot fungus ... grows really well in a warm, dark, moist environment. That's the inside of a shoe."
Finally Cody Lundin, of Dual Survivor fame, who is "an outdoor survival-skills instructor who has gone barefoot for 20 years". He observes that "if the irritation gets bad enough, it will stop you in your tracks. That would be unacceptable for a hunter population."
PopSci stops short of saying that human evolution took a wrong turn when it started wearing footwear, since the resulting epidemic of Athelete's foot forced hunting expeditions to be curtailed. (I suppose that Lundin is an example of present-day human evolution that is making a proper course correction). Or perhaps evolution took the right turn, since the irritation of the fungus caused humans to turn from hunting to settled agriculture. I suppose both points of view would be acceptable to evolutionists (it's amazing how evolutionists always have the correct answer, whether its yes, no, or both).
In the midst of all this hard core information, what really stands out is the admission that people had decent footwear going back to just about the time of Adam and Eve!
Here is a far more likely explanation: Cavemen are not the right folks to talk about. When Adam and Eve were expelled from the Garden of Eden for their rebellion against God, God clothed them with the skin of the first animal that ever died. They were extremely intelligent, since they were created in the image of God, and quickly figured out that in their new harsh circumstances, they needed to cover the other parts of their body, like their feet. And yes, after the Fall, they did get athlete's foot!
To see the PopSci article, go to http://en.calameo.com/read/0001278539e10d1809223, click on the search icon in the upper right, search on "cavemen", then select page 104.
P.S. This "scientific" article is not to hard to read, and is only two columns long. However, I'm wondering how scientific it is. Here are some difficult science words that it contains: "good guess", "probably", "I don't imagine that", "could have" (3 times), "might have" (3 times), and "sometimes". If you read it, make sure you don't stumble across these words too badly.