Now this is an interesting (the terminology in the field is "valid") question.
But you want to think about th following:
a) What does it mean that the universe evolves from finite initial conditions? Finite initial conditions also means an infinite set of conditions specifying finite values for the relevant variables.
b) Assuming that the universe expanded from a finite "size", what is the "initial size" consistent with Sharon's theorem?
c) It is (wildly) believed that the amount of information present in the "initial" state of the universe must be the same with the amount of information that we see today, based on some sort of information conservation theorem, which would somehow resemble the conservation of energy theorem. How would a steady state approach to energy conservation would affect your reasoning, if one were to consider that inflationary cosmology is a valid theory of the Universe evolution.
Yhink about this, dkv, and also think about the fact that this is a problem that both "gravity" people and "quantum information/computing" people have in their sights (i.e. there is a multitude of sources adressing this problem that you might want to consult)
