We're already doing this - to an imperfect degree
The question of whether or not the universe is deterministic has already been covered so I won't step into that argument other than to agree that we don't know the answer to that and won't ever, simply because the universe is too big and complex to be able to resolve that question perfectly.
But; there are parts of the universe that we have been perfectly predicting for some time. We know (for example) not only the exact length of a day, but how much it is changing over time as the earth's rotation slows gradually. We add leap seconds into atomic clocks to keep them in sync with its rotation. We know when the moon is full, when it's new, well into the future. We know what will happen to the sun over the coming 5bn years and what impact that will have on the Earth.
We also can predict things like fraudulent transactions out of a sea of financial data, which emergency service workers are at a high risk of self harm or other consequences of stress. We can predict how a patient will react to a given medication, and we can predict what the world will be like in 5yrs, 50yrs, 500yrs if we keep burning fossil fuels and continuing our population growth. I already do many of these things personally with analytics algorithms and AI.
All these problems are what we call narrow domain problems; that is to say, that they operate in a very specific way that can be segregated from the universe as a 'job lot', meaning that if the rules that govern them and the stateful data that those rules can be applied to are both present, we can know what the future state will be in these cases, with varying degrees of accuracy.
That is to say that;
1) The more discrete the problem is and
2) The better we understand the problem and
3) The more complete our state data is then
the more accurately we can predict the future according to that specific domain. We know that some causes seem to have consistent and specific effects. We would never have invested so much money in the Apollo program if we weren't positive that putting human beings on top of that much fuel wouldn't have finally put them on the moon, for instance. Physics does seem to act in many ways deterministically and for the purposes of such grand endeavours, can be trusted to deliver a specific effect when we apply a specific cause.
Of course, every model is a simplified version of reality in some form. For the most part, we simplify by only modelling those parts that are relevant to the domain of problem we are solving. BUT, we also simplify by subsetting the data to the larger cause/effect pairs, knowing that reduces the accuracy of the prediction.
So; in any prediction, the completeness of our understanding of the rules and the completeness of our understanding of the initial states both impact the accuracy of our prediction. If both are perfect, then the prediction will be perfect but in reality, we know that's not the case. We often make do with 1:1m chance or even lower as being 'perfect' knowing that this will be close enough for our needs.
If I remember correctly, The chances of a conventional SATA HDD not recording a 0 or 1 correctly is somewhere around 1:10^38, making it virtually perfect, at least for our needs.
So, ultimately, we already can and regularly DO predict the future, we just do it within relative subsets of the universe AND with slightly less than perfect predictions.
Now, to get to the universe itself. IF (and it's a big if) the universe is deterministic, that means that there is a set of rules that govern it. If we can know those rules perfectly, then all we'd need is a complete set of state data for the entire universe to model it.
That would look very much like - well, the universe.
In other words, we'd probably need a full universe in order to be able to model the universe perfectly. That is because the universe is already very efficient in recording its internal state, and mimicking that would require something even bigger to store the data on, so another universe would probably be your best bet.
Of course, if you're after less than perfect outcomes, you can use a smaller set of data. As discussed at the beginning, we already do that to predict the orbits of planets, moons, rockets, et al.
So, if the universe is Non-Deterministic, then all the above is invalid. You'll never perfectly simulate the universe because it doesn't conform to any rule set. BUT, as has been already discussed, we have rules already that get pretty close to perfect, so if the universe isn't deterministic, it's probably not off by much.
What does all this mean? Well, it means that the universe is sufficiently deterministic to make almost perfect predictions about parts of it, which is what we do every day.
Ultimately, this follows an inverse square law. Eventually, you're pouring far higher levels of model sophistication and data into ever decreasing improvements in accuracy. We deal with these problems in advanced analytics all the time, and the answer is that you provide the most accurate answer to the widest domain that your data and the understanding of the problem will support.
Usually that's enough. How wide a domain you're seeking to predict will ultimately define just how much data you need, and whether or not it can be managed within the cognitive limits of a human mind or the processing limits of a computer.