"And, Buddhists claim, there is no chronological first beginning to the series of past lives. We have all of us been reborn an infinite number of times. No God is needed to start the series off – for there simply was no first beginning. Things have been around (somewhere) for all eternity."
I feel this is a wrong grasp, somehow. In the assu sutta the Buddha says:
"From an inconstruable beginning comes transmigration. A beginning point is not evident, though beings hindered by ignorance and fettered by craving are transmigrating & wandering on."
He says that the beginning is 'inconstruable' and 'not evident', and indeed I recall reading that on the night of his full enlightenment, no matter how many lives and World-cycles he looked back, he could find no beginning point...but that isn't the same as saying that there is no beginning point, just that it's fruitless trying to pin it down.
There are many instances, such as this one, where the Buddha, rather than offering our intellects an answer to every single question they might thirst after, invites us to redirect our gaze to what really matters - as when he says, (following on from the last quote):
"Long have you thus experienced stress, experienced pain, experienced loss, swelling the cemeteries — enough to become disenchanted with all fabricated things, enough to become dispassionate, enough to be released."
Then the Blessed One, picking up a tiny bit of dust with the tip of his fingernail, said to the monk, "There isn't even this much form...feeling...
perception...fabrications...consciousness that is constant, lasting, eternal, not subject to change, that will stay just as it is as long as eternity."