Yeah these are all things I have thought about in the past. I don't think we can even begin to grasp what eternal or the concept of infinite is so I don't believe I can answer your question. The time we are alive in this world is not even a fraction of a grain of sand on the universal timeline.
I've always had a feeling that something "was up" though in reference to your cattle pen/lab rat analogy. I've given up trying to think too much about these things because I will never know the answer.
