Are there any notes from experimentors in antiquity trying to build the hottest fire in the world, capable of reduing Iron to liquid?
2000 BCE seems firmly in the age of antiquity.
From https://acoup.blog/2020/09/25/collections-iron-how-did-they-...:
"The second problem is chemical, because we are never going to melt this iron. Our furnaces can’t get that hot (and even if they could, melting this iron would cause it to absorb a lot of carbon from our fuel, which we do not want). So we’re going to be reducing our iron – that is, getting it to change chemically with the exposure of heat. That means the chemical composition of our iron matters a lot and we have to solve our chemical problems before we can smelt our ore.
The good news is that some ores of iron reduce fairly easily and directly, most notably hematite and the hydroxide-iron ores like limonite and goethite. They reduce fairly easily (but the latter two tend to come with lots of water that needs removing). But then we have magnetite, which while also an iron-oxide, doesn’t reduce nearly so easily as hematite, and siderite (and other carbonates) which has carbon in it, which we do not want. Moreover, our country rock might have some trace amounts of things like sulfur (or iron-sulfides) in them, which we very much do not want. Sulfur will absolutely ruin our final iron product, so we do not want it floating around when we get to the smelting process."
...
"The place and time for the discovery of iron smelting is not known, partly because of the difficulty of distinguishing metal extracted from nickel-containing ores from hot-worked meteoritic iron.[2] The archaeological evidence seems to point to the Middle East area, during the Bronze Age in the 3rd millennium BC. "
https://en.wikipedia.org/wiki/Ferrous_metallurgy
Even the source you linked mentions actual smelting as early as 900BCE. Just because it wasn't the most common method doesn't mean it wasn't known or possible.
Smelting does not imply that the iron or iron ore is ever in a molten state.
I can imagine over the centuries, a lot of people dedicated many years of their lives to pursuits like this, most of which went nowhere, and probably some were based on interesting models of the world such as phlogiston or etc.
The situation gradually improves post-Renaissance, but we don't even have any contemporaneous writings about how Newcomen designed and built his engine in the early 1700s - just second-hand information from decades later.