Yeah, I'm pretty sure that's answered in the documentary too. You should watch it. There are several ways to approach it.

Given that there will be an infinite number of present times, then it is logically conceivable that an infinite amount of time has elapsed for each one of them. The limit of the past present time doesn't have to be the present time that you want to pick up, because that would be confusing and switching the necessary condition with the sufficient condition. I know, it gets confusing, that's how the logic works. This is only by resorting to Logic and Philosophy, not Physics. You can watch the documentary for more information.