Dear 100 Hour Board,
Let's say humans invent a time machine and want to travel back as far as they can in the earth's geological history. Obviously, modern humans didn't evolve until, like, two million years ago, but what's the earliest period that would have been able to support human life had it arrived by means other than evolution? How far back could the time travelers go if they wanted to find a world hospitable to their taking up residence there?
One quick thing: you're correct that about two million years ago (1.8 million, to be precise) saw the emergence of the first Homo Erectus, but modern humans as we understand them actually didn't evolve until about 300,000 years ago. But you're right, if we were to travel back in time, we probably could have survived on the earth long before that.
Now let's take some time to talk about human dietary requirements. The three macronutrients humans need in their diet in order to survive are protein, fat, and carbohydrates. As long as there were animals around to hunt, getting protein and fat wouldn't have been too hard, but carbohydrates are another problem. My guess is we would have to wait at least until angiosperms (flowering plants) developed for a really reliable source of carbs. The first angiosperms developed in the Cretaceous Period, or about 125 million years ago, so humans would probably have to wait until then. Conifers have existed on the earth long before that (dating back to about 300 million years ago), but probably wouldn't have been a reliable source of food because they take so long to germinate and then grow, and aren't as nutrient-packed as angiosperms. Also, to clarify--when I say that angiosperms are flowering plants, I'm not just talking about garden flowers here. Almost all shrubs, trees, herbaceous plants, and grasses are angiosperms; or in other words, about 80% of all plants on earth are angiosperms. They're a big deal. They probably wouldn't form the backbone of our fictional time travelers' diets, and meat would remain the staple for probably millions of years more, but having them around would probably be necessary to sustain any sort of human life. So let's put the earliest limit for humans at about 125 million years ago, or 100 million to be safe, if we want to wait until angiosperms really became prevalent.
The again, if humans were to go back to the Cretaceous, it's likely that we would have been wiped out in the KT extinction event (the asteroid that killed the dinosaurs), so we'd probably want to wait until the Paleogene started (66 million years ago) before trying to colonize prehistoric earth.
Ecology reserves chiming in here to (mostly) second Alta's answer. I really enjoyed this article about some emerging thought on the diversification of mammals. Still puts major developments after angiosperms taking off (125 million years ago ish?)
We started getting close around 500 million years ago (mya). But it's less of a progressive time line and more of a series of windows. There were plenty of fluctuations that could kill a human population. Asteroids definitely help, but they have friends. Nailing the right time window would require much more precise estimates of a million factors. Getting it right becomes less likely the closer to 500 mya we get because of increased uncertainty and decreased precedence.
The first breathable air was starting to occur about 500 million years ago. But how close that air was to a modern human's preferred 78.09% nitrogen, 20.95% oxygen, argon (0.93%), carbon dioxide 0.039%, and other trace gases (0.003%) is another question. Here's a nifty infographic on human tolerance for temperature, humidity, oxygen, and pressure. Those are pretty narrow parameters, and our estimates of those times are very uncertain. Temperatures are especially tricky. But honestly since around 800 mya I think there have been some manageable temps. So I'm still okay with estimating 500 mya.
Food is another argument. To really allow for the persistence and development of a human colony, I think Alta is pretty much right. They need a reliable source of food that doesn't take too many resources to acquire. 500 mya they had some kinds of fish, but there wasn't much diversity.
500 million years, fish and proto-amphibians;
475 million years, land plants;
400 million years, insects and seeds;
360 million years, amphibians;
300 million years, reptiles;
200 million years, mammals;
150 million years, birds;
130 million years, flowers;
Maybe we could get by eating some small diversity of fish, insects, and seeds. Let's give ourselves at least another 100 million years to diversify the diet. Soo, 400 mya?
This is a short clip about what happens when humans only eat meat. We might be able to work out some of those fiber issues, but honestly the glucose stuff is indeed very real. Especially if we're talking about the propagation of a human culture.
So basically your question is a fun one because there is no straight answer but plenty of variables to talk about. I've contributed some information to think about but there's so much more! If I were making an official recommendation to society I would tell them to delay a chartered expedition until we had used time travel to sample an acceptable number time frames and locations. We could get the statisticians involved to decide what that acceptable sample number might be, and then decide the time that would give us the largest window of time before an extinctive event occurred. It shouldn't be too hard to find something worthy of our settlement if you consider how long we've been on the earth compared to the length of the ages and changes were aware of. Regardless of settlement efforts, even a few trips to sample these time frames would help nail down our geologic timescale a TON.
Keep conjecturing! Conjecture is the primary provision of intellectual fun... and misinformation. But whatevs.