big bang theory - Could the universe have evolved differently?

I don't think your attempt to distinguish the micro and macro scales is helpful. As it stands, the physical theories (quantum mechanics etc) are deterministic, that is the initial conditions pre-determine all future: there is no random element ("Gott würfelt nicht" -- god does not throw dice -- to quote Albert Einstein).

Of course, this is debatable, but certainly beyond astronomy, better (meta)phyiscs and philosophy ...

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Edited to respond to the comment, effectively rephrasing the question to consider a "slighly different" early state of the universe.

Well, it pretty much depends what you mean by "slighly different". If the laws of physics are completely untouched, I would think that the universe would evolve statistically in exactly the same way. This is because all the statistical characteristics of the early universe (the power spectra and correlation functions of the various energy densities, for example) come about from the laws of physics (via natural instabilities, for example) rather than the initial state.

However 1, our understanding of the laws of physics and their deeper origin is still very limited. This means that it is not clear whether a slightly different early state with exactly the same laws of physics is actually at all possible. This is particularly true for the nature of gravity and the vacuum, neither of which is currently properly understood at the quantum mechanical level.

However 2, one has to bear in mind that we don't know whether the universe is finite or infinite. If it is infinite (and the observational evidence from our finite patch of the universe indicates that it has a flat or open, but not closed, spacetime), we cannot really make any sensible conclusions from our finite observable patch. This includes this answer!
Except, of course, if we invoke an extended version of the cosmological principle, something like "an infinite universe must be the same everywhere", which is (meta)physical non-sense. This is the main reason why I don't like cosmology too much.