| | Well, in order to describe time, you need events with which to measure time. Saying that time has a 'beginning' steals the concept of time as dependent upon an ambient existence in which things play out. So in that sense, time cannot have a beginning.
As far as an alternate notion of time, I've read A Brief History of Time by Stephen Hawking, and he makes mention of some kind of 'imaginary time' using imaginary numbers as opposed to real ones. However, such a thing has no physical significance and is a mathematical tool.
In any case, there is absolutely no evidence of the universe being created from nothing, Big Bang advocates notwithstanding. If there turned out to be something that predated the Big Bang, well, then whatever it was, it must have existed, and so ought to be part of the universe.
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