There is a significant number of people who reject compatibilism (the idea that determinism and free will is compatible). If compatibilism is false, given a deterministic universe, this would imply that free will doesn't exist. But we don't even need to suppose a deterministic universe to reject the concept of free will.
I would argue that the idea of free will is a thoroughly dead concept, that simply doesn't make sense given our modern understanding of reality, causality and the brain. At this point, it's merely a nice idea, that seems important, without any remaining rational grounding.
Let's suppose we can reproduce a state of the universe down to the last atom, boson and whatever else. If someone is given a choice and they act differently the second time around, this would imply one of the following:
They have some existence outside of the universe. This does little more than introduce something we didn't reproduce (that we also don't have compelling evidence for), rather than actually solving the problem. To address this, we can simply extend the hypothetical to suppose that we also exactly reproduced any existence external to the universe.
Their actions have some random element. This may meet the requirements of the problem, but acting randomly does not match what we think of as "free will". We certainly wouldn't call a random number generator "free".
I do not see any other option.
Something is either deterministic or random. If it's deterministic, it would be the same every time we reproduce it. If it's random, it's not "free".
Barring randomness, if we reproduced them exactly, with every desire and thought process that they had at that point in time, and we put them in the exact same situation, they should weigh up the available choices in the same way based on their identical desires, and end up making the same choice.