Who says there is no beginning or ending of time? The Big Bang says just the opposite.
You missed the part of our conversation where our universe may not be the only one. It may not be the first, there may be as many or more than there are galaxies. We may have been seeded from a preexisting one. Which would make time proceed the big bang, and the one that proceeded us, and the one hat proceeded that one. And this cycle has always been and will be perpetual with no beginning and no end.