It's very possible to have a computer simulation of a universe, although this universe probably not one, for many reasons.
Firstly, there doesn't seem to be any evidence here that shows that our minds are connected to something external, although now that I think of it, perhaps there doesn't need to be.
Secondly, we certainly don't have free will here, because that would require our minds to defy the laws of nature and do whatever they want for no reason, so I wouldn't see any point in a universe simulation except for research... This also means that if we are connected to a simulation, then our 'real selves' aren't having any effect on the decisions we make here, they're just experiencing our senses and thoughts.
Thirdly, if this is a simulation, the chances that the creators of it are human is seriously infinitely improbable, given that humans have been around for a microsecond in terms of evolution, and the universe is rather large, and there's probably other life.
If there ever was a simulation of the universe, it would not have active agents connected to it. There wouldn't be any point unless it was a small-scale simulation, and not a universe simulation. It would only make sense to have active agents connected to a simulation if it were for training or recreation. Proper simulations of a universe would definitely be standalone, with nobody connected, because having people connected would instantly defeat the purpose of a true, natural simulation entirely, unless the people inside it were unable to control their person, and only experience it.
I think if we worked out the precise conditions of the big bang, and simulated it on a ridiculous computer, you could fast-forward and watch life begin on Earth, the dinosaurs become extinct, humans evolve etc. etc. etc. What would really boggle my mind though, is if we fast-forwarded into the future, with the intent of discovering new technology that we come up in the future - a paradox. I now think we will eventually either become too smart for our own good, or we'll continue to destroy our own planet with nowhere to go.