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We don't know if the universe had a beginning or not, but we can observe that the past is more ordered and the present is moving towards disorder. We don't know why.

That would seem to be a beginning.

And by "time began at or about the Big Bang," I mean, "time came into existence as part of the Big Bang, depending on how you define 'Big Bang'."

I've become more interested in the philosophical concepts of time is a function of consciousness. Donald Hoffman talks about this a lot and in terms of our limited experience within 4 dimensions, 3 dimensions of space and one dimension of time.

Space and time are aspects of our universe. What we perceive as spacetime doesn't exist outside our universe. Thus, expansion is into nothing...at least, the expansion is not into more spacetime.

I suppose a secular analysis must say we just don't know what that nothing, or something, is. Some might add "yet," although it is not that we don't know yet, but that we don't even know how to discover and test that yet.

A religious analysis might say that outside of our universal spacetime is something which theology calls Eternity. According to one theory (which does not disagree with the latest physics theories, but which is not confirmed by them either), Eternity is a timeless existence in which God resides (because time only exists in, and part of, our universe). It's not that God exists forever; rather, it's that He exists outside of time and space. Thus, time unfolds for us within our spacetime (and if we could perceive outside of spacetime from our current vantage point within spacetime, it might appear that the things we observe exist for all time, but it is more than that...they exist outside of time).

Fun stuff to think about.