The classic argument for determinism is that there might be an equation of everything that perfectly describes everything on any level. We just have to find the initial conditions, build a big machine and run it until we get to the current time. From there we could calculate all actions from everyone and eventually determine our future perfectly.

There are several issues with this.

Universe Machine

It is impossible for a machine in a closed system simulating itself completely. As the information of the full system needs to be stored it would use the full system for storage, making the machine itself reality.

Also without an outside perspective the contained data cannot be fully understood. Another assumption needs to be made, namely that a subset of the universe can be calculated in isolation. Like a single planet.

Initial Condition Problem

This creates another problem, that of the initial conditions. Without a time machine it is impossible to know on all scales where everything was located exactly at the time of the start of the simulation. And even if it would be, what about cosmic dust hitting our earth or other outside factors like solar storms?

More simplifications need to be made and proven to be applicable, that those influences do not matter in the simulation range or are on scales that do not impact the outcome.

To make the size of the simulation domain even smaller we can further reduce the problem to a short period of time for few people where everything is known perfectly by using some kind of scanner. The people willing to be simulated need to be isolated from outside influence as well.

Deterministic for Whom?

Finally we have reduced the problem to a scale that might be possible to simulate in the universe itself, but who is actually perceiving the determinism? If the people have access to the machine and can ask it questions to answer about the future, what would happen?

The answer the machine gives is new information introduced into the closed system, altering the course of the simulation and we are back to the initial universe machine problem where the machine is contained in itself.

What are we asking?

This means the actual problem about determinism is not really grounded in physics. It might be possible as outlined to construct a machine like that, but the actual question is one of fate.

It is about the grand idea that maybe something is pulling our strings or something put an imperceptible order on our lives and that we are bound in our lives and purpose to a specific outcome.

The Machine's Purpose

This separates the actual philosophical thought from physics and the only physical question is if a simulation is possible on the detail level described. The machine itself would be only useful for looking at the past or other parts of the universe.

But in doing so a whole other question might become answerable. It would be possible to prove if physics alone is responsible for our lives without any influence from anywhere else by checking the calculated outcome with our history or other isolated systems.

Outside Determinism

Knowing that all your actions can be computed and predicted theoretically by someone far removed, would that change your behavior?

The far removed watcher would not be able to do anything with this information as it would change the prediction. In a sense they would have a complete history of you, without any need to wait. Like a biography of everyone. I leave it up to you to decide if this is great or terrifying.