Not since the Big Bang.
Your question seems to suggest that you accept the idea of a Big Bang, since you use the term 'Big Bang' as a reference to time.
The concept of infinity also is used in reference to time. unending time.
Time as we perceive it began at the instant of the Big Bang. Along with space. The space we see out there that we call the universe, with all the energy and matter contained in it, which seems to be fated to expanding ever faster with time. Time as we know it.
We think of time as time forward or time back. We seem to think of infinity as time forward. Knowing what we believe to be true of the universe, today, during our time, makes it difficult to think of an infinite time in the past because of our concept of the Big Bang. It is an indelible reference point in our mind when we try to conceive of the universe and its beginning, in time. Time back. But to a point. Not infinitely back. An infinite future time is not so difficult to imagine.
If this time is the only one we can perceive, and we can see that at this time ( a manifestation of space-time), there is all this expanding space with all its energy and mass (again, two manifestations of the same thing), then we must accept the notion that there is something, not nothing. At least since the Big Bang.
The instant of the Big Bang, the beginning of time and space, ended the possibility of an "infinity of nothing". All of a sudden, there is something.
In any discussion of infinity-eternity-everything-nothing one should research the concepts of "dimensionality and branes". Try looking up M-theory.
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It does, or it can, suggest an infinity past. It is no less reasonable to theorize a past infinity as it is to theorize a future infinity. We convince ourselves that a future infinity is meaningful while a past infinity is not, but this comes more from the limitations of our minds than anything else. Either way you are talking about an infinitely long stretch of time, with one terminus in time.
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True. Any further discussion must surely include the possibility that our universe was born in the 'Big Bang' event, and that the 'Big Bang' itself occurred when two 'branes' collided in a larger 'multiverse' of eleven dimensions. But if you go into that particular discussion, you must discuss gravity and it's strength relative to the other known physical forces, and perhaps the idea that gravity is a force acting within and throughout the 'multiverse' and distributed in some way between all the universes that exist within said 'multiverse. The other thing we don't wanna' discuss here then is the concept of 'time' as it relates to the 'multiverse'. Makes me shudder.
