ruthless,
To a certain degree yes - we can create a virtual universe. Physicists do that constantly through math and through computer models.
There are many problems involved with modeling the universe accurately so that it evolves exactly as our universe has evolved. Here are some examples of the problems.
One concept involves observability. We can only observe so much of the universe even with the most powerful telescopes. There are areas of the universe so far away that even though the light from those areas of space have been traveling toward Earth for ~18-20 billion years it hasn't arrived here. We can only guess at what went on there. Its pretty hard to figure that into the model. And we have no idea what is going on "now" even in our own galaxy because the light that shines on us from the nearest star, other than Sol, is 4 years old.
Another problem involves "The Three Body Problem". We can model a universe that only has one particle in it. That particle does precisely everything that we expect it to do. We can add a second particle to that universe and still model what goes on quite well. But when we add a third particle their interactions become very complex. With great difficulty we can model very accurately what occurs if we don't ask the model to look very far into the future. Once we get to ten particles it's virtually impossible to sort them out, tell one from another and predict anything specific about what an individual particle is going to do. A glass of water has about 10^24 subatomic particles (protons, neutrons and electrons). That's 1,000,000,000,000,000,000,000,000 - an incredibly huge number. We can use the principles of thermodynamics to make predictions about the glass of water in general but there's absolutely no way to say anything specific about a single atom of water let alone the protons, neutrons and electrons that make up the atom. Extend that idea to the entire universe of 10^99 particles (1 followed by 99 zeros) and modeling what will occur at any time by asking the model to precisely recreate our universe in detail is impossible.
A third problem involves our knowledge of physics. We know an awful lot about how the laws of physics work. But we don't know everything and some of what we know only describes what happens and not what causes it to happen in detail. Because our knowledge is incomplete any model that we create will be incomplete to some degree.
Thus modeling the entire universe can be done using the laws of physics as we currently understand them but there's no guarantee that the universe that evolves in the model would look anything like the universe that we know - even though the laws of physics would be the same.
The issue of time traveling in the virtual universe goes to the third problem. We can force the issue in the model and plug in "laws" that allow time travel. But in the real world we don't know enough about the underlying physics to be able to state that time travel back in time is even allowed. We have certain solutions to general relativity that say that under very unusual circumstances it is possible. But those same solutions also say that the universe as we know it today isn't the same sort of universe described in the solution.