But you are inside the universe. The mathematical structure of the universe can contain all of your perceptions and to you they will "feel real". Indeed, to you they are real.

If you had a perfectly accurate universe simulation, do you think the people inside the simulation would not be conscious?

If they're not conscious, it's not a perfectly accurate simulation.

And if it is possible to have a perfectly accurate simulation, then (like you said) all of the contents of the universe were "there" all along inside the giant mathematical structure. You don't need anyone to run the simulator!

All of the contents of the universe, the apparent flow of time, our thoughts and feelings, our consciousness, all lives inside this incomprehensibly large mathematical structure.

This is how I believe reality works. The universe exists inside mathematics the way 42 does. You don't need a calculator to show the number 42 in order for the number 42 to exist. Running the simulator can expose the contents of the universe to someone outside it, but everything on the inside is independent of the simulator.

You might ask "why this reality and not any other?" and I would say they all exist equally well, we just happen to notice this one because we're inside this one.