Imagine a line segment, let's call it a timeline... now does the non-existence of the line past its endpoints invalidate the timeline itself?
For the analogy to apply, imagine you have an infinitely large sheet of paper, with its edges at infinity.
If I asked you to draw the line segment with its first of two end points (one being the “origin” of Time, “Big Bang”, etc., and the other representing the present moment) at the centre of the page (the other end point being radially away from the centre) how would you find this centre?