In an infinite by infinite plane it simply doesn't matter because the [non-existent] edge is an infinite distance away from any given point. IOW, the origin is arbitrary and may legitimately be said to be anywhere -- thus arbitrarily deciding/defining that the "start of time" point is the origin is valid.
Think about it some more. If the infinite plane has a centre that could be anywhere, then everywhere would be a centre. But can this be true? Our Universe is infinite - it has no “edge” to define its limits. If anywhere was its centre, then right now you are in the centre of the Sun.
But you obviously aren’t. So, even in infinities, centres matter. Likewise, Time cannot be “begun” without a pre-existing Time to define the change that brings about the new Time’s existence. Change, put in simpler words, is simply impossible without the lapse of Time.