It had never really occurred to me before that you can pile most of your earthly possessions up in a box somewhere with "PLEASE TAKE" stenciled sloppily on the side, but you can't really do the same with a plot of land.
Don't forget tribal governments.
Well, until you die, at which point you can't legally own property anymore and the ownership automatically reverts to someone else.
Post the signed paperwork to transfer the deed on the door, make the price one dollar, and whomever signs it now owns it.
Technically there’s no consideration unless they actually give you the dollar, but as this is impossible to demonstrate in court, it should be ok.
In 1660, John Locke published his Two Treatises of Government, where he set out to resolve the seeming conflict between individual property rights (which he valorized) and the Bible (ditto), which set out the principle that God had created the Earth and its bounty for all of humanity. How could a Christian claim to own something personally when God had intended for everyone to share in His creation?...
In collective/national terms, Iceland and most of Tuvalu could count - genuinely uninhabited territory settled by ancestors of the people who live there now. (Tuvalu was a British Crown colony, but on some of the smaller islands that doesn't seem to have actually changed much.)
As far as "the same group continuously owned this acreage", I was sort of stunned to learn that parts of the Fort Apache Reservation probably qualify. The White Mountain Apache entered the region perhaps 100 years after the Mogollon population completely abandoned it to drought, and have apparently held it for 500+ years since without ever being removed by war or the US government. Even legally, it appears to have been held by the tribe collectively (and acknowledged as such by the USG) throughout history.
There likely remain properties in Europe which can trace ownership through at the very least centuries, if not 1000+ years.
Possibly some British Crown posessions.
I would argue that six of Tuvalu's nine islands are reasonably clear cases. The current Polynesia inhabitants have a direct line of ownership back to the first arrivals. Tuvalu was a British protectorate and then crown colony, but it remained comparatively independent until actual self-rule - and as far as I can tell, British colonial administrators never extended beyond the islands of Funafuti, Nanumea and Nukufetau, nor did American soldiers in WWII. The remaining six inhabited islands appear to have been consistently controlled by the first people ever to settle there.
If we discount strictly paper claims of ownership, the number may go up - some remote regions of some mainland indigenous land don't seem to have ever been meaningfully contested. In North America, some parts of Nunavut or non-coastal Alaska are the most obvious options.
More surprisingly, the White Mountain Apache appear to have held some land from continuously from European arrival to the present Fort Apache Reservation. The pre-European history of the region is somewhat less clear, but it appears that the Mogollon residents of the area abandoned it during a drought around 1400, before the Western Apache moved into the empty region. If so, that represents continuous ownership for around 500 years with no initial conquest.
Note that taking national possession of an entire island need not necessarily displace all, or even any, prior / traditional land claims or rights.
My interest at this point is more in suggesting possible places to look than in claiming "this is definitely where that is the case".
Usually land ownership emerges as a concept alongside the development of agrarian cultures. If you're going to spend time cultivating land, you tend to want to defend it.
The initial African diaspora occurred before historical records were being kept. Odds of either African or non-African land claims matching the condition of both being Terra Nullius and being documented through their entire history of possession are ... slim.
Historically recent island instances are more likely: Pitcairn, Falklands, St. George, etc. Azores as another response notes. Iceland is among the earliest virgin colonisations of land not previously permanently inhabited which has been documented from its start. I don't know enough of its specific history to know that it fits the conditions of continued lawful ownership transfers.
Mainland North and South America fail as they were previously inhabited. The various British Crown possessions are generally newer than Iceland, but might qualify under the lawful transfer requirement.
There might be instances along the Aleutian or Kuril island chains, though I doubt it. Possibly islands north of Siberia as well, though some might consider Communist rule a chain-of-ownership break.
https://en.m.wikipedia.org/wiki/Adverse_possession for the complexities.