“Where and when would you most like to visit to witness and analyze an event in Earth’s history?” Suppose you have a space-time machine to (safely and comfortably) watch an event unfold; which event would you most like to see? Why? What do we already know or hypothesize about that event that appeals to you, or that you would like to test? What would be the result, the upshot, of knowing more about this event? You do not necessarily need to limit yourself to Earth, nor to the past. You do not need to limit yourself to a particular instant if peeking several times over a period of minutes or ages helps you envision the evolution of something. You do not need to limit yourself to environments that could support life as we know it... imagine being able to take a time-sampling of magmatic composition from 10 miles below the surface as a nascent mid-ocean ridge opens up, or examining the circumference of the vent during one of Yellowstone's mega-eruptions! I'll tell you, this technology is basically magic.
I would like to go back, not to the Big Bang (which I would assume several scientists would love to marvel at) but before it (maybe a few billion years, give or take). What came before the Big Bang? Was there just a singularity sitting there for all eternity or was the previous universe collapsing in on itself? This would help answer the current question of whether the universe is going to expand continuously or eventually stop expanding and start collapsing in on itself.
My time and place is this:
Or was it really just a large guy with a white cloak and big beard thinking what he should do next?
"How bout an incredibly dense piece of matter? I wonder what would happen if I made one of those?"