However, in order to reach a point in time it is necessary to move through all of the previous points in time. It is not possible to just appear in any moment in time that you see fit. Therefore, by the very fact that we are existing in this point in time indicates that we have already past through all of the previous points in time. Since you are considering to time be extending infinitely in both the past and the future, you are necessarily stating that the Universe has moved through an infinite amount of time. This is not possible.
This is mere conjecture and a typical human perspective. In no way is this backed up by physics. There is no evidence or suggestion of a master time, T, that ticks its way from the the past to the future. Such a concept is in fact in direct contradiction to General Relativity. We exist at our own time in the Universe, and that is all we can say. But this is a deep topic and this is not the place for its discussion. Suffice it to say that your argument is insufficient to suggest that the Universe does not extend infinitely far back in time.