I think the confusion is pertaining to what whether the reference is to this present Universe or any other. The finite origin of this present Universe is what is agreed upon by many. However, nothing is known of what existed prior to the Big Bang, and that is the point which can accommodate a cyclic model.
Physicist Neil Turok: Big Bang Wasn’t the Beginning
http://www.wired.com/science/discoveries/news/2008/02/qa_turok
For decades, physicists have accepted the notion that the universe started with the Big Bang, an explosive event at the literal beginning of time. Now, computational physicist Neil Turok is challenging that model — and some scientists are taking him seriously.
According to Turok, who teaches at Cambridge University, the Big Bang represents just one stage in an infinitely repeated cycle of universal expansion and contraction. Turok theorizes that neither time nor the universe has a beginning or end.
It’s a strange idea, though Turok would say it’s no stranger than the standard explanation of the Big Bang: a singular point that defies our laws of physics, where all equations go to infinity and “all the properties we normally use to describe the universe and its contents just fail.” That inconsistency led Turok to see if the Big Bang could be explained within the framework of string theory, a controversial and so-far untested explanation of the universe as existing in at least 10 dimensions and being formed from one-dimensional building blocks called strings. Within a school of string theory known as m-theory, Turok said, “the seventh extra dimension of space is the gap between two parallel objects called branes. It’s like the gap between two parallel mirrors. We thought, What happens if these two mirrors collide? Maybe that was the Big Bang.”
Turok’s proposition has drawn condemnation from string theory’s many critics and even opposition from the Catholic Church. But it’s provoked acclaim and wonder, too: He and Princeton University physicist Paul Steinhardt published Endless Universe: Beyond the Big Bang last year, and Turok — also the founder of the South Africa-based African Institute for Mathematical Sciences — won 2008’s first annual TED Prize, awarded to the world’s most innovative thinkers.
Turok spoke with Wired.com about the Big Bang, the intellectual benefits of cosmology and his bet with Stephen Hawking.
A closed universe would accommodate a repeat cycle; however, it still leaves the gap at the beginning of the cycle, singularity, no time/space, as well as the metaphysical gap of the cause of the cycle.
We're on the edges here of both physics and human conceptual capacity. Greater minds than ours struggle to even fathom the possibilities.