There are two possibilities for our universe's history.

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There are two possibilities for our universe's history. Either there has always been some matter and the existence of our universe filled with some sort of object recedes infinitely far into our past, or at some point the matter and objects that fill our universe emerged from nothing. If the former then the theory is proven: Time is infinite. If it is the latter however, then at some point objects emerged and history began. From there we face three possibilities:

1. The universe comes to a finite end, the existence of space filled with matter is bookended by infinite nothingness
2. The universe is swallowed into nothingness and eventually another universes emerges as did the one prior
and lastly,
3. The universe never dies and we have an infinite future ahead

Now, shrewd readers will have noticed that in fact scenarios 2 and 3 are essentially identical. Or more accurately, the second scenario develops into either the first or third scenarios. The peculiarity of scenario 3 is that it subsumes the fragments of scenario 2. Put another way. An infinite universe would, by it's very nature, contain all the staccato'd universes from the second scenario.

Here lies the crux of an otherwise perfect and succinct proof of time stretching out infinitely; Starting from the assumption that our universe at some point emerged from pure nothingness, we have definitive, self-evident proof that the possibility for something to emerge from nothing exists. If the possibility exists for it to occur once, there's no real reason to believe it won't happen again. To be fair, there's no real reason to believe it will happen either. It is, for all intents and purposes, an ontological coin flip whether we live in the only universe that will ever exist, ever, for all eternity or whether we will live within a universe that lives forever.