The Random Factor

Is it really possible that our universe is not deterministic? Some physicists, especially quantum physics pioneers including but not limited to "Niels Bohr", claim that our world is not deterministic, and actually includes a probabilistic random factor. Many physicists, including but not limited to "Albert Einstein" one of the founders of the quantum theory refutes this indeterministic factor, and suggests the existence of a "local hidden variable"... thus Albert Einstein apparently supports the deterministic view of this world, and agrees that there is no such thing as unpredictability. (source)
The local hidden variable theory supports my personal view that: "Uncertainty is the direct consequence to lack of knowledge." (read more)

Yet, I find one stone in the road: In accordance to my personal understanding of the world, and assuming that the universe started as a singular point as the theory of big-bang suggests, its is very tempting to conclude that the universe should exhibit perfect symmetry.... Obviously our world has nothing to do with symmetry: A perfect symmetry is like a perfect sphere; our world is nothing like that! It is tempting to associate lack of randomness with symmetry... So does this mean that there is actually a "random factor" in this universe?

To better understand the argument it is useful to understand the basic assumptions:
1- Determinism
2- The world started as a singular point
3- A singular point is necessarily symmetrical
4- Expansion of the singular point under deterministic physics laws leads to universal symmetry
5- Lack of randomness implies symmetry (in other words, asymmetry needs randomness)
6- Determinism defies *deep* randomness (consider)
7- The universe is not perfectly symmetric

This argument is probably flawed; or maybe not.... The weakest link I think is the 4th assumption that expansion of a symmetrical point needs to be symmetrical under deterministic physics. Also the 3rd assumption that the singular point was symmetrical is not necessarily supported by big-bang theorists...

Please share any scientific or philosophical (or otherwise) views on this issue.... I am too eager to find a satisfying answer to this counter-determinism argument!

PS: The scientific validity of this post is NOT asserted