I think you might be overstating your case a bit. Non-Western cultures don't have as much an emphasis on things having a clear beginning, middle, and end, the cosmological claim that the universe clearly must be temporally bounded is not even the dominant stance for modern day inflation theorists. There are other alternates (eternal inflation [1], 'big bounce' [2], etc.)
I think part of the confusion stems also from language. A multiverse where other 'universes' are physically accessible to us in principle (if we're willing to wait long enough or go far enough), should that really be considered another universe? On the other hand, there are even parts of our current space-time that are so remote that we will never see them—so are they other 'universes'?
As a counterpoint, Chinese culture certainly focuses more on the inherent cyclicality of things—even beginnings and ends are embedded in a larger cycle that may not have bounds. “话说天下大势,分久必合,合久必分” It is said that in the great scheme of the world, that which is long divided, must unite, and long united, must divide
> Scientists later determined that this proposal implied something strange: that the multiverse is infinite, with endless, uncountable parallel universes existing alongside our own....
This is the first time I'd heard of that proposal. It rings true to me (I know—naturalness is another word for the truthiness fallacy) in the sense that the outer reality needs to transcend time and therefore—if our universe is time-bound—contain infinite time-bound sub-universes whose origination and final fate are not externally bound by time. Or perhaps the "no-boundary proposal" is just a succinct way of saying that!
> That wild situation presented a number of problems for science, most significantly that it rendered most basic scientific ideas about the multiverse impossible to test. ...
> "Hawking was not satisfied with this state of affairs," Hertog told Live Science in March. "'Let's try to tame the multiverse,' he told me a year ago. So, we set out to develop a method to transform the idea of a multiverse into a coherent, testable scientific framework."
This reminds me of Einstein's discomfort with true unpredictability—"God does not play dice"—how he helped lay the foundations for quantum mechanics but never fully accepted it himself because it was too weird (as I understand it—I'm a rather poor historian).
> Hawking's final paper suggests a framework for understanding the universe that would render the multiverse finite, countable and subject to meaningfully engagement via the tools of science.
People claim it as a proof of "God" or a creator, and I used to be skeptical of that logic (albeit I am a theist, for other reasons) but the way you put it I find pretty convincing.