I was thinking about this too. There's actually something called the Poincare recurrence time, which is the approximate amount of time it would take for a region of spacetime the size of our observable universe to just pop into existence based solely on quantum effects. Unsurprisingly, it's extremely long, involving a power tower of about 5 tens, with a 1.1 at the end. At this length, units don't matter, because whether you use Planck times or years, the difference doesn't really affect the exponent.

Of course, that's nothing compared to infinity, literally; however, there are several problems. First, it's not known if time would still exist in any meaningful sense at this point, since all that would exist would be distended and scattered particles. Owing to the rapid expansion of space, these particles would eventually get so far apart that no particle would be in any other's observable universe and thus no causal contact could be made, and hence you might argue that no time could exist because no longer would there be any way of measuring or observing it. Also, the Poincare recurrence would be much shorter for a region of spacetime much smaller, like the solar system, which would be all we need to exist, hence the question of why our own universe is so large if this presumably wouldn't be the first cycle. One possibility is that there are no cycles, because the PRT does not exist; or, potentially we may live in a multiverse with new regions emerging all the time so the bulk of matter ends up existing in "young" universes, while older ones that have achieved maximum entropy or heat death occasionally experience small spontaneous entropy decreases that amount to only tiny fragments of all matter present.