Yes, there are some infinite sets with both upper and lower limits. These are not, however, relevant to the present discussion, where we are debating the existence or otherwise, of infinite regress. It doesn't matter, for our discussion, whether any given bounded period of time can be divided into an infinite number of smaller parts; the question is, is time unbounded in the past. I am ignoring the irrelevant, for the sake of simplicity; I advise you to do the same.
Time that has a beginning and an end is not infinite regress, regardless of our ability (or otherwise) to divide it infinitely, for the same reason that the arrow hits the tortoise, regardless of our ability to divide the distance it travels into an infinite number of fractional parts.