Anything isn't possible given an infinite amount of space and time if there are constants/laws governing it within it. The four fundamental ones being gravity, electromagnetic, strong and weak forces, whose laws do not change given infinite time or space.
You can have an infinite amount of possibilities without including everything conceivable being possible. An infinite amount of time and space does not mean any thing you can imagine, such as a person being smaller than a single atom or that light stops reflecting, will happen.
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To the question posed in the title : In a universe of infinite space and time [and I would add matter], is it possible for something to happen once?
The simple answer is : Yes, if the probability that the event happens more than once is zero.
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I agree. For example, if all the universe contained was a bomb, and it detonated then no matter how much time and space you give it, those particles will never meet again, let alone undo irreversible reactions into a re-formed bomb.