It's got to begin somewhere, in the first pass neither Elizabeth nor Charlotte exist.

The only way for either to exist is for Young Noah to meet Young Elizabeth, but Elizabeth cannot exist without Charlotte existing first.

Young Noah cannot ever meet Elizabeth, because, future Noah, and future future Noah, and future future future Noah would have had to as well.

How many cycles have already past? Is the notion of this whole plot that infinite cycles have past?

That's the only explanation I can accept to explain the paradox. Because if it happens in infinite cycles into the future, it doesn't need an explanation because there can never be one.

Not simple, there is no beginning. The beginning has to theoretically be somewhere, and that only theoretical somewhere infinitely into the future.