I think there are probably a number of ways to answer this question depending on how you define various aspects of it, but I'll have a go as best I can since its a very interesting question.

You asked about the early West Asian civilisations, but I think its quite unlikely any of these would have had any truly empty land to expand into, as early civilisations arise mostly in areas that have been inhabited for a very long time, and the civilisations of the middle east arose in areas which had been home to Neolithic farming communities for thousands of years.

By definition, in some sense, all parts of the globe must have had first inhabitants who moved into an area before anyone else did. However, it is very difficult to find many concrete examples where there is sufficient evidence to know what group of people arrived first, and when.

In Eurasia and Africa, much of the land had been inhabited by archaic humans for hundreds of thousands or even millions of years before Homo sapiens arose. Its conceivable that one could argue that the dominant wave of Homo sapiens which is thought to have left Africa around 70-80kya moved into uninhabited territory in the sense that they would only have encountered different human species (with some exceptions such as sapiens already thought to inhabit Arabia and the Levant). However, there is a lot of evidence to suggest these humans were not that different, such as genetic evidence that Neanderthal and Denisovan populations interbred with Homo sapiens, and fossils in China from the middle Pleistocene which have features which have been interpreted as showing that they left some genetic mark in modern east Asian populations. So I would argue these areas cannot really be seen as definitive examples of Terra Nullius.

So, what about the places that Homo sapiens were the first human species to arrive at? There is no evidence any other human species reached Australia or the Americas before sapiens did, so in some sense there must have been an initial 'Terra Nullius' arrival in these places. However, this is also complicated and hard to trace. Evidence increasingly pushes back the date of first arrival of humans in these areas, (at least 18kya and possibly as much as 30kya for the Americas, and at least 65kya and possibly as much as 100kya in Australia), and in both cases it looks like there were probably multiple waves of humans, some of which may have left little trace on either the genetic or archaeological record. So, while by definition some group of humans must have been the first to either of those places, we can't definitively say when that happened, or whether or not those first inhabitants left much lineage in modern indigenous Australia or America people.

That said, I can think of a few definitive answers of places which were almost certainly completely uninhabited prior to colonisation by groups of people recently enough that we can know at least broadly when and how it happened.

Firstly, the Polynesian migrations in the south Pacific took them to a number of islands, mostly notably New Zealand, which were almost definitely completely uninhabited when they arrived. This is a clear example of an advanced society settling in lands without displacing previous inhabitants, and establishing new societies in those lands.

Another example would be the Norse colonisation of Iceland. While the exact reasons for this colonisation and how it happened are a bit murky, due to most relevant sources being from later in the Medieval period, it is pretty clear that they were the first people to inhabit the island on any sort of significant scale, although there have been controversial studies that suggest limited numbers of Irish colonists might actually have reached the island first.

Finally, there are a few genuine examples of Terra Nullius from the age of European colonisation (although not many). Some places colonised by Europeans, mostly islands in the South Atlantic, genuinely were completely uninhabited when they arrived. The Falkland islands, for example, are thought to have been uninhabited when first colonised by the French.