I actually want to directly challenge this point... that you'll be dust before the subject is ever withing reach of expanding human capacity. Chances are, it'll be well within your life time that it is.
Since the moratium on Nuclear Weapons testing in 1992, the United States Department of Energy has spend hundreds of millions of dollars, every few years, developing and deploying increasingly powerful supercomputers. These computers have been used to, with greater accuracy as computers improve, simulate the geometry of a nuclear explosion to ensure "reliability" of our stockpile as they age. These computers have over the years, also been used to simulate climate patterns, phyiscs phenomenon, protien folding, and everything else that requires large numbers of simulated data points.
So why do we keep building them? Why aren't the computers from 1998 satisfactory? Why did the DoE open Titan, the most powerful supercomputer in the world, just the year? It's because of resolution. As computers increase in power, new techniques are developed to simulate phenomenon at increasing levels of resolution (smaller and smaller scales), in a hope of increasing the accuracy of their predictive models. Going with this is the development of new techniques to ensure the model is a valid one.
Today, when scientists simulate galaxies or galactic collisions, their resolution is typically stellar level. 15 years ago, it was groups of stars. Ten years from now, it may be of sufficient resolution to simulate resolution far lower than that. I'm sure you can see where this is going.... So the day comes, in the future, where the resolution of the universal simulation is so small that it is simulating information about state inherent to all sub-atomic particles that is a fundamental building block of any universe (and why a 10^500 universe is information dead, because it never gets transmitted). You've successful modeled an actual universe to the point you've created one.
It's a theory, provable actually, but so-far unproven, that our universe is in fact, a two dimensional computer simulation. And the theory is valid to the point that there is no reason that a future human, in possession of advanced technology, couldn't build a computer that does the exact same thing. It's mostly a matter of scale - the larger the simulated universe, the larger the energy requirement and so forth.
Does the chance we're living in a computer simulation infer intelligent design? Absolutely not. Even if our universe were a subset of a greater universe, and that upon a greater-greater universe (yes, this is essentially turtles all the way down), there exists a universe where all laws are natural. And even within any existing program, there are natural behaviors that are emergent with the properties of the system... no intelligent design required. The same is exactly true of the universe. If this sounds like a chicken-and-the-egg paradox, it is in part.
The point is though is that just like building a Solar System sized particle accelerator, or building a 3 foot wide wormhole to Alpha Centauri by annihilating Jupiter and capturing all it's mass-energy, simulating universes in a computer is a problem of scale and resolution, and both, if you're only ambitious to a point, are extremely within the realm of possibility. After all, if the Copernican Principle holds true (and there is no reason to think it doesn't), there is no need to simulate a universe , and the sextillion galaxies within, unless you're interest in the change over time of the large scale structure of the universe. If you're interested in almost anything else, a medium sized metal rich galaxies will do, and thus you've already cut the problem's complexity (and energy requirement) down countless orders of magnitude.
Simulating how the the universe works at extremely fine resolutions is not something even close to being beyond our capacity. At issue is mostly a matter of application. Right now scientists are still figuring out the nature of Dark Matter and Dark Energy, so the need to do the mega-simulation hasn't yet arrived, unlike say, Climate Change, which is very much interested at the present in seeing how global climate change effects climate at smaller scales than the entire planet.