Creating a computer simulation that determines whether life could have evolved in a given amount of time amounts to creating artificial life. My answer is a qualified no, it is not feasible for us to determine whether two billion years is a sufficient amount of time for life as we observe it to have evolved naturally--as opposed to evolving under direction of a "guiding hand". I answer with a qualified no because the recent sub-field of computer science known as Artificial Life has in fact made some impressive progress. We are nowhere near simulating anything more complex than single-cell creatures, but simulations have been carried out which do seem to adequately model some aspects of biological evolution and natural selection. Populations of programs let loose in a computer's memory were able to optimize their own code to reproduce more efficiently. Other interesting analogies to biology have also been observed in these simulations, such as the emergence of parasites--programs that exploit the code of other programs to do their reproductive work. But there is still a great deal of controversy about whether these efforts will ever shed light on biology or whether they are just "elaborate games with little relevance to the world outside of computers."
So in this sense, the question of whether there exists a "guiding hand" in the evolution of species remains an open question. But it is really the *lack* of any such "guiding hand" that is the heart of Darwin's revolutionary idea. The wondrous complexity and Design that we perceive in nature arose by purely mechanistic (or algorithmic) processes. As Darwin put it in a letter to the geologist Charles Lyell shortly after the publication of _The Origin of Species_: "I would give absolutely nothing for the theory of Natural Selection, if it requires miraculous additions at any one stage of descent.... If I were convinced that I required such additions, I would reject [the theory] as rubbish..." Before Darwin formulated his theory of natural selection, it was inconceivable how something as complex as, say, a human, could come to exist without being designed by some pre-existing Intelligence. Ever since Darwin, it is now clearly *conceivable* that the guiding hand doesn't exist, but there is also obviously still some doubt. It is my assertion that any undiscovered principles still needed to explain the emergence of life will necessarily be mechanistic ones. Assuming a pre-existing Intelligence is simply begging the question: Where did Intelligence come from? So the hypothesis of a guiding hand can never lend insight into the process of evolution.
To approach the question of "enough time" from another angle, I would refer to the writing of Stephen J. Gould on the fallacy that complexity is the goal of evolution. From our perspective, it is easy for us to imagine the process of evolution as leading up to the creation of humans--adding more and more complexity over billions of years. In fact, this is not at all the case. Humans are at the end of a very particular branch in earth's family tree which does happen to value complexity as a selective advantage--for example, the ability to conceive and design tools is something which requires an incredibly complex brain. But bacteria are actually much more fit than humans for survival as a species. Consider our comparative chances of surviving nuclear war--suddenly bacteria don't seem so inferior. And yet bacteria haven't had the need to evolve additional complexity for the past billion years. Clearly then, our preference for complexity is subjective and aesthetic. So what, exactly, are we asking if there was enough time for? We do know that the mutation rate of our DNA is more than enough to account for the actual displacement between our genomes and those of our simplest ancestors. But this is like saying that if we attempt to change the word "CAT" into the novel "War and Peace" by changing or adding one letter per year, then a billion years is more than enough time to account for that much typographical difference. Of course, typographical distance between ourselves and amoebas is not what we are interested in. But since we've established that what we *are* interested in is subjective, then marveling at the result of our path of evolution is putting the cart before the horse. It would be like defining our alphabet with a random sequence of letters and then marveling that that random sequence could just happen to come out in alphabetical order. So without having an objectively defined outcome that we are measuring, the whole question of "enough time" becomes moot.
In conclusion, I find the hypothesis of a cosmic Intelligence unnecessary for a scientific understanding of the evolution of life. Although it is not yet feasible to confirm this with a computer simulation, I feel that it will eventually be possible to do so. But even if it isn't, there are sound scientific and philosophical reasons why the God hypothesis would not be a solution. First, it is begging the question to posit something infinitely complex in order to explain complexity in nature. Second, the question of whether there was enough time for humans to evolve can be answered with a definite yes in the trivial sense of genetic difference from our earliest ancestors, and any other sense depends on a subjective decision about what kind of complexity is important. So, while my grandfather and I agree that evolution is the primary cause of the diversity and complexity of life, I am willing to embrace it as the sole explanation for our existence.