Our current understanding of Entropy seems to suggest that there exists an arrow of time. The amount of entropy in the universe cannot decrease: it can only increase until the universe is in complete thermodynamic equilibrium. The argument is that if the universe was infinitely old, thus never having a definite beginning, the universe as we know it now could not exist, because the universe's entropy would be at a maximum and no energy transfer could take place.
However, that in itself seems to be a problem. How is it that the universe had such a low entropy in its very early stages? The big bang theory predicts that the universe developed from a singularity and at the time of its creation, had an extremely high temperature. So, why didn't the universe remain in thermodynamic equilibrium from its very beginning?
I would also like to add my opinion that the Big Bang never happened. There may be a process on a much larger scale which can reverse the Entropy of the universe, and if so, this could allow the universe as we know it to exist eternally and thus it may also not have had a beginning. It is an interesting question as to whether the universe has existed eternally or not, we do not yet know for sure. What are your thoughts?