Who claims that we presently find ourselves in a “cycle” that is really still embedded in the infinite future??? I think we simply presently find ourselves in a cycle or epoch of a forever-lasting history of existential reality (or series of epochs of causally-connected existential realities) in which we DID happen to arise and in which we presently DO languish.
Said another way, for me the question, “how could there ever be enough time for us to reach the particular cycle we are in,” is the wrong (illegitimate but sounds legitimate) question (similar to Zeno’s “paradox” which is not really an actual paradox).
For me, the right question is: How can the history of existential reality NOT be from an infinite past…???
Not saying existential reality could not even possibly have popped-up uncaused from a genuine state of universal timeless nothingness – I’m saying -I- cannot find or imagine any good reason (…nor even any bad reason…) for giving that proposition even a moment of non-zero serious consideration – that proposition (even if true) is of no value to me whatsoever (as it explains nothing and even if it true it is not knowable). Not even an “utter, clean-to-the-bone re-setting(/”rebooting”) of epochal clocks does not logically require that there was once universal timeless nothingness – indeed it seems to me that if logic bears on the question at all logic requires that there never was timeless nothingness (else a static stasis of timeless nothingness would still universally prevail).
I could be wrong of course (who among us is infallible?), but there’s my feeble, fallible present thinking for what little it may b worth.