I just want to remind you that unlike the Tech Tree in Civ, humans don't evolve linearly. I'm assuming you are asking how many people with how much technology can you have without leaving an impact?

Apologies in advance if this answer violates the rules.

Human technological civilization could not have advanced very far and then been "wiped out", only to occur again. Simple logic makes it clear that, just for instance, a previous civilization couldn't have used much petroleum... when this resources started to be exploited in the 1800s, deposits were very shallow in places like Pennsylvania and Texas. A previous civilization would have used these up (they're the easiest to get to), leaving nothing behind for us.

It's also true that a civilization that discovers how useful petroleum is will probably devise drilling techniques to allow them to also remove more difficult deposits as well.

This is not true only for oil. Coal and natural gas are similar in these respects.

This is not true only for fossil fuels... many important metal ores are the same way. Tin and copper would be the first, most likely, to be depleted.

So all the ancient astronaut crap is just that, crap. Technological civilization can probably only arise once on a given planet and certainly only once in any 100 million year period or so.

Again, if my comment is inappropriate, please delete it and accept my apologies. I like this place, I don't want to be banned.

All human civilizations (that we are aware of) leave some sort of impact on the landscape. So there in turn are three basic questions that archaeologists and anthropologists must answer in order to find that trace of a lost culture.

1) What sort of evidence has the culture left behind?

Monumental architecture is hard to miss, but what if the culture built primarily with wood? Did the culture use metal or stone tools? Has oral history survived beyond the decline of said culture? Think Germanic Baltic cultures, Pacific Northwest First Nations, as examples.

2) How fast has the landscape changed?

Pompeii and Thera were buried under dozens of feet of ash. There may even be settlements under the Black Sea. There is research underway (going off Charles Mann's 1491) uncovering ancient settlements under the Amazon canopy using ground penetrating radar. Those latter two examples may be as close as we get to "discovering" lost cultures unknown to us.

3) What are we looking for?

This is big and is related to number one. While the archaeologists of the late 19th and 20th century were transfixed by Minoan and Egyptian architecture, the far more ancient Danubian and Ukraine agricultural cultures were almost totally unknown. It took a while for archaeology to advance and start looking seriously at the small potatoes: clam shell deposits, slash-and-burn activity, holes in the ground which may have contained wooden posts. Science caught up to with radio-carbon dating and GPR. Who knows what we might be looking for and with what in fifty years.

I hope this answers your question or at least provides better insight.

What is it are you asking exactly? That advanced ancient cities like the late 19th/early 20th century idea of what Atlantis was like existed?

Well, anything later than the pyramids isn't going to work. The problem your going to run into further back than that (and other obvious structures) are primitive hunting techniques. Humans have been building fish traps and animal herding walls all over the world for a very long time.

Even a relatively simple civilization would have likely used these as well. Did they line their homes with rocks? What about their fire pits? Did they use stone tools? At this point you are well past history and more into archaeology.

Sorry, this one is a little too speculative for us, we're more for the dry, dusty and cite-able answers here, but you should check out /r/HistoricalWhatIf!

I'd say up to the early 19C. It would have to take place in a region which was either cleared by glaciers, or submerged by rising sea levels following an Ice Age. This isn't a big constraint, as most of our recent centres of civilisation have fallen in one or the other category.

It could not have had a major impact on resource depletion (coal, iron ore), hence that as a target date. It might go a bit later in areas with substantial organic substitutes for metals. See for instance current-day China, which uses bamboo for many purposes we would use metal for: scaffolding and building material; irrigation "pumps" and distribution; cutlery; etc.