One possible way to explain the arrow of time is to say that the entropy is increasing simply because the entropy in the beginning was at unsustainably low levels and is therefore bound to increase. The way that the entropy got so low in the beginning can, in turn, be explained by postulating special conditions that prevailed at that time---such as cosmic inflation, high density, extreme temperature, or others. Without going into the details of such explanations, there seems to be a general objection that could be raised to counter any explanation in that direction. The general objection is that space-time homogeneity should rule out special conditions anywhere in space-time, including the very onset of time itself.
Therefore, my question is this. How do we reconcile the principle of space-time homogeneity with the intuition that time can only have one origin?