Possible? Sure. Probable? Not very.

Settled, agricultural societies leave very specific traces. This involves not just the remains of buildings, but also tools, pottery, weapons, burial practices and a host of other evidence. If there was a developed culture with urbanization we would have found archaeological evidence in those places which are ideal for human habitation, such as the Middle-East, India, China and Mediterranean.

Civilizations do not just vanish without leaving anything behind them, and no large scale geological catastrophes have occurred that could have erased evidence within the last 20,000 years as it had around 300 million years ago with Lizardoid culture. Little is known about Elamite and Proto-Elamite culture, but there is plenty to prove they existed. There is Chogha Zanbil:

http://whc.unesco.org/en/list/113

And we have their clay tablets

https://oi.uchicago.edu/collections/photographic-archives/persepolis/cuneiform-tablets#Captions

And pottery:

https://commons.wikimedia.org/wiki/Category:Proto-Elamite_pottery

Keeping that in mind, let's look at Göbekli Tepe. It is very old, 10,000 years or so. A developed civilization would have left multiple Göbekli Tepes at a variety of sites, and would have left evidence similar to that of the Elamites. That we have not found any tends to point to no "lost empire" having existed. Remember, an organized state society would have left a lot of artefacts to discover.

So the thing is that places like East Asia aren't exactly archaeological wastelands, even if they're wetter. Sometimes that's actually a bonus - for example, a site now known as Kuahuqiao was preserved by being waterlogged, so we know for example that the people of central China used canoes 8000 years ago.

We have significant archaeological evidence for the Late Neolithic (very roughly the third millennium BC) on the areas of China that are the geographically most ideal for complex, unequal societies. The lower Yangtze was home to the Liangzhu culture. From archaeological evidence, we know that the Liangzhu culture emerged northeast of a lake called Lake Tai and spread south of the lake. We know that the Liangzhu farmed rice. We know that they had large settlements; to quote A Companion to Chinese Archaeology on a particularly large site, "[this site] can be seen in relation to other sites of the Liangzhu culture as one would contrast a modern city with neighboring villages" (this claim may be disputable, but you get the general gist). We know they had a stratified society which some archaeologists have termed a kingdom, we know they loved jade and that jade had a particular symbolic significance for them, we know their elite population gradually increased, we know they had pictographic symbols which most scholars agree did not constitute true writing, and so on. We know in broad strokes that it ended abruptly for disputed reasons and even that there might have been some Liangzhu refugees who fled south during the collapse.

I'm ranting a bit here, but my point is that we know a lot about what cultures and societies existed in China or especially Europe at the time. Sure, there are big and surprising discoveries, but I can't readily think of any recent ones that invalidated decades of intensive research on the entire, relatively well-documented culture. If Liangzhu turned out to be something like Old Kingdom Egypt, it would overturn decades of intensive research on this entire culture we believe we know a fair bit about.

So yes, it's possible, but it's unlikely.

ETA: Just wanted to recommand The Archaeology of China: From the Palaeolithic to the Late Bronze Age

To address your friend's argument about preservation bias:

1. Very few ancient texts are known from preserved, ancient copies. We generally know about them because they were continuously read, copied and re-copied through the millennia. There are notable exceptions would like the Dead Sea Scrolls or the Epic of Gilgamesh, but these aren't the foundation of our knowledge of ancient civilisations. And when we're talking really old (and the earliest civilisations do belong to prehistory) our main or sole source of evidence is archaeology, not texts.

2. It's not nearly so simply as dry areas are better at preserving evidence. Some things are better preserved in dry conditions, some aren't. As an archaeologist working in an arid area of the Middle East, I'd kill for the kind of organic and sediment preservation you get in temperate Europe.

Unrelated question about that map: it shows the Hittite culture and bronze-age Greeks, both of which among others broke off from the Indo-European culture iirc. Are they the steppe pastoralists east of the Caspian Sea? Because that's not where I've heard the commonly-accepted theories place the early Indo-Europeans. Or had the original IE tribes all migrated from their traditional homeland by 2000 BCE?

How well does this question translate to the new world?

Or has the existence of such societies been ruled out by other forms of evidence?

Follow up. Has any historian or archeologist actively looked at questions like that (for Europe or elsewhere)? I know that a non-scholarly answer to the first part of OP's question, "Sure it's possible, but there's no evidence for one."

But absence of evidence aside, is there any particular line of evidence that would tell us there wasn't one? Obvious resources that weren't exploited until later? Early documents confirming an absence of civilization? Evidence that agriculture couldn't have started prior to a certain time? What sorts of "evidence of absence" could there be?

What about the flooding of the Ur-Schatt valley? Rose's narrative would suggest to an uninformed layperson that there could be some really interesting stuff underwater in the persian gulf.

J. I. Rose, New light on human prehistory in the Arabo-Persian Gulf Oasis. Current Anthropology (2010), doi:10.1086/657397.

As a small methodological point unrelated to the substance of the question posted by OP, I want to point out that the issue of selection bias in (especially ancient) history is a really important, and under-discussed topic among historians. There is an inevitable way in which historical data are sort of collected and collated especially where there aren't a wealth of new discoveries of evidence in a particular field. But that this also compels historians to operate within the de facto selection of historical survival is an important historiographic issue to raise. A good example, for instance, is varieties of pre-Christian sectarian communities in the Eastern Mediterranean. We have some remarkable evidence from various sources, but in the 20th century, the Dead Sea Scrolls have become the dominant resource for understanding what they were and how they operated. However, the Qumran evidence leaves contemporary historians with one relatively contiguous example. We still speculate on the hows and the whys of sectarian identity, community formation, and practice based on the DSS, but there is no question that it is an impossibly limited sample, and shouldn't really dictate how we understand "sectarian communities," so much as a series of communities that operated in the same area of the Levant.

Anyway, I'm laboring the point, but I think it's worth noting that the issue is very much relevant, esp. for ancient historians. And yet––and this can be frustrating for people outside of the guild of historians or those from other historical specializations––we do sort of have to live in the tension of our lacunae-filled evidence. We frequently have a spotty record, but it is still the record we have, and we have to make the conclusions that we are able to. Sometimes this forces us to make estimations or broader assumptions than is ordinary in other disciplines. But it is almost impossible not speculate and, as it were, accept the biased nature of what time has selected for us to have.

(Written, not edited. Pardon typos and infelicities.)

On a semi-related note, does anyone have more maps like the one OP posted? This one was really fascinating to examine.

Question: According to this map, the Indus valley civilization is nomadic pastoralists. I always thought they were atleast simple farming societies. Didnt they settle along the Indus river because of its fertility?