Is there a definitive answer?

No, there are no definitive answers yet.

Our species goes back at most 200,000 years, so any "300,000" year dates you've read don't refer to our species. Of course, "intelligence" may predate our species, depending on how you define "intelligence".

The oldest manufactured tools are from Gona, Ethiopia, dating 2.7 million years. They are very crude, so I'm not sure they represent what you mean by "intelligence". They were made by Homo habilis, which had a brain the size of a chimp's. Possibly Australopithecus also made tools.

Th earliest evidence of the controlled use of fire goes back to about 750,000 years, to a cave in Israel where several hearths were found, as well as evidence of long human occupation. Burnt grains suggest humans were cooking. Lots of flint chips indicate humans were using the fires for illumination to work by. There are some earlier dates going back to a million years, but they are less well accepted.

Does the controlled use of fire represent intelligence, in your view?

The beginning of symbolic or abstract thought is difficult to define, since they left no writing behind. Anthropologists use various artifacts as proxies for it, though it's an open question exactly what such artifacts mean.

For example, do pierced beads represent symbolic thought? Shells and beads of various kinds, pierced with holes to string together into a necklace or chain have been found dating to over 100,000 years in both north and south Africa. Some people may argue that making necklaces shows that these people had a sense of esthetics, which means they must have been capable of abstract thought.

There are stones etched with lines in geometric patterns from at least 80,000 years ago in south Africa. There are objects that were deliberately colored with ocher. Do they represent "intelligence"?

At around 70,000 years we have evidence of non-trivial planning, in the form foraging tidal flats in south Africa. Anthropologists think they indicate the human ability to predict tides, which is not easy. It requires keeping track of time and some calculations. This seems pretty much like intelligence. From the same period, we have fire-hardened tools, where common but poor quality raw materials are hardened to improve their characteristics by burying them under hearths before chipping/shaping them. That seems like intelligence to me as well.

From 50,000 years we have a lot of evidence from the Aurignacian - primitive musical instruments in the form of flutes, figurines, and somewhat later, cave paintings. These must surely be signs of intelligence.

So it's kind of a matter of how to interpret these very old artifacts and understand what they mean, and also a matter of how you define intelligence.

Many anthropologists think that the evidence of abstract thought in the form of carved and decorated stones, beads, etc. is convincing, and indicates that people were capable of "modern" thought and behavior at least 100,000 years ago.

But then you could argue that perhaps our current limit of 100,000 years is just the result of old stuff being incredibly rare, and that these dates will be pushed back further as more discoveries are made. In fact, why shouldn't they be pushed back all the way to the dawn of our species, at 200,000 years? We don't have any solid evidence that our brains have changed to suddenly enable "intelligence" recently. So perhaps the ability to think in modern terms is simply a feature of Homo sapiens, and has been around ever since modern humans have been around.