Is Determinism Compatible with the Big Bang Theory?

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This discussion explores the compatibility of determinism with the Big Bang Theory, specifically questioning how a homogeneous state of matter at the universe's inception could allow for determinism. The argument posits that if the universe's state at time $t_1$ can be determined from time $t_0$, then the initial conditions at the Big Bang must contain sufficient variables to support this determinism. The inquiry challenges the notion that a singular, homogeneous state can lead to a deterministic framework, suggesting a fundamental conflict between these two concepts.

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  • Concept of initial conditions in scientific theories
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After watching a Sam Harris conference a question came to my mind.
Maybe it's been discussed several times, but I couldn't find any of that.

The starting point is that, according to determinism, the state of the universe in instant $t_1$ could be theoretically determined knowing its state at a previous instant $t_0$.
Well, let's take it for granted, which is not by the way.
Let's go back in the past, where every instant is predetermined by the instant before.
We may eventually arrive to a beginning, let's say the big bang.

Question is: what if all the matter at a certain moment (the first moment) was in an homogeneous state ? If all the matter was compressed into a hot dense sphere of homogeneous matter, then how can determinism be true ?

Otherwise, there must always be, in any moment, as much variables, as we find in a successive moment, otherwise it's not possible to determine the causes of the actual state of universe.
Is then determinism compatible with big bang theory ?
 
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