In order to simulate the future of the universe, one would need a computer that could store every bit of data required to express the state of the universe, plus anything required to handle any temporary calculations and then extra if you want to store anything about that simulation.

There is only one such device known to exist: the universe itself. And it doesn't store any simulation history, though you can figure out some things by examining the current state.

We could simulate a smaller portion of the universe, but you still need to store every bit of information about the current state and things would diverge anyways because you won't be perfectly simulating the edges and those differences would cascade throughout the whole thing eventually.

That state for Earth would still take an earth amount of matter to store. But ok, let's say we repurpose Jupiter to be a perfect Earth simulator at least until the edge differences mess it all up, plus it has a ton of extra matter to store useful information about the simulation. First thing you'll need to do once it's ready is initialize it with the current state of Earth.

But, there's a problem: how do you measure every single thing about something without the earlier measurements changing the later ones? You can't measure something without interacting with it in some way. Even if you just look at it, it changes (though it's not your eyes that change it, it's the light that bounced off of it to get to your eyes). That change is miniscule for direct affects on us, but it's very relevant at a perfect simulation level of detail.

The universe might be deterministic (I don't think there's any real way to determine this for sure either way, like what would be different if it was or wasn't?), but it's not prederministic, at least not from within.

Maybe there's some kind of mechanism to see a reflection from the future or something like that, but even then, what would happen if someone saw themselves walk through the left door in the future but when the moment came walked through the right door instead?

Well a crap shooter is most likely to roll a seven, so I dunno about your analogy.