The main difficulty with iron is that higher temperatures are needed for smelting, compared with copper. Additionally, smelting takes place in the solid state, and the product will either be a spongy bloom full of slag, and techniques to turn this into usable iron are needed (nothing too fancy, basically just hammering and folding), or cast iron, which is brittle. The main advantage with iron is that the ore is very abundant compared to copper ore. (And, eventually, you learn to make steel.)

Pottery is the likely precursor to both copper smelting and, where it developed before copper smelting, iron smelting. Kilns for firing earthenware can reach temperatures high enough for copper smelting, and stoneware kilns high enough for iron smelting. For both copper and iron, smelting might have been discovered from the use of copper and iron ores in glazes, which can, in a reducing atmosphere in the kiln, yield metallic copper and iron. There is no need for intermediate steps with metals with lower smelting temperatures, since pottery alone can be sufficient motivation to develop hot enough furnaces for copper and iron smelting.

Working native iron (usually meteoric but sometimes telluric) is unlikely to evolve into iron smelting. Combined with a tradition of stoneware pottery, it would make the development of iron smelting more likely, since iron produced from pottery glazes would be more likely to be recognised as useful, but without high temperature pottery furnaces, or existing copper smelting technology, the key technological requirement - suitable furnaces - would be lacking.

In addition to sub-Saharan Africa as already noted by u/Commustar iron smelting appears to have preceded copper smelting in much of South-East Asia.

Yeah, for basically all of Africa south of the Sahara, there was a direct transition from stone to iron technology without an intervening copper or bronze age. African peoples did develop copper working and bronze/brass working techniques, but those seem to have developed (or learned) at the same time or after iron was introduced.

I wrote about this with reference to sources in this thread

First, some background on the discovery of Copper and Tin metallurgy. Copper and Tin ores are frequently unusual, interesting, and attractive rocks. They are unusually colored (Copper ore is often green or blue) or lustrous and angular (in the case of the Tin ore Cassiterite). They're the sort of thing that curious and inquisitive people would collect and experiment with. And these ores are also very straightforward to "accidentally" smelt. All you need to do is heat them in a reducing atmosphere to around the melting point of the metal. You'll then transform the ore (typically an oxide) into the metallic form, while melting the metal will allow it to separate from impurities in the ore, producing and refining the metal in one go. Making use of a "reducing atmosphere" may sound very technical and sophisticated but it turns out all you need is some Carbon Monoxide, which is an excellent reducing gas, and forms quite readily inside of a fire with an excess of charcoal. You can smelt Copper ores in an ordinary campfire simply by placing it deep inside and running the fire a little on the hot side (for Tin it doesn't even need to be that hot).

From there it's a pretty straightforward shot toward learning how to improve the smelting process, learning how to re-melt metals to pour into casts, learning how to combine multiple metals to produce alloys with different properties, learning how to make better casts, improve the edges on cast weapons, etc, etc, etc. All of that is a process of simple iterative trial and error tinkering which flows naturally out of the basic discovery of smelting and working these metals.

This overall process works for these metal ores for a couple reasons. One, they have low melting points. Most especially they have lower melting points than the silicate "glassy" minerals which often make up the major impurities in the ores. That makes it easy to differentially separate the metals from their impurities. It also makes it easier to reach the temperatures necessary to smelt the metals with simple furnaces and fires. Also, they are very amenable to casting. Cast bronze, for example, is a hard and corrosion resistant metal that can hold a sharp edge, making it useful in a huge variety of tools and parts.

Now, it may seem as though Bronze working naturally flowed straight into Iron/Steel working, and there's a little bit of truth to that but mostly it's an artifact of chronology. The core problem here is that smelting and working Iron is trickier with more pitfalls and the easiest route to working Iron is very different from working Copper, Tin, and bronze. If you try the techniques above to smelt Iron you'll run into several very serious problems. Fortunately, reducing with CO works just fine with Iron ore, but that's about the only thing that will go right. Unfortunately, the melting point of Iron is very high compared to Copper, which means you need a much more specialized furnace design to reach such temperatures, and you have to put much more work into it (to provide air flow to the heating flames to keep the temperature up). Worse, smelting directly to molten Iron leaves you with a mess full of impurities because silicate glasses as well as Iron oxides melt at the same temperature or lower. On top of that, the metallurgy of Iron is very complex, because typically you have a bunch of different crystalline forms of Iron-containing minerals (often along with Carbon), each of which has different properties. Simply taking Iron, even very pure Iron, and pouring it into a cast is unlikely to produce high quality tools or weapons (though it can make adequate pots and pans).

The simplest low-tech way to smelt Iron is via a bloomery-furnace. You still need to get the temperature well above the melting point of Copper, which takes some work. You'll need a proper furnace and you'll need some way of forcing air into the heating part of the fire. Then, you take your Iron ore and surround it with charcoal (in some methods you make a paste of ore and charcoal slurry) and you place it above a larger amount of wood fuel in your furnace. The goal is to immerse the ore in a reducing atmosphere while heating it not to the melting point but to the welding temperature. The ore reduces to become metallic Iron which welds itself together into a sponge or "bloom". As you reach the right temperature some of the silicate impurities in the ore will melt and run out of the bloom, while some will remain. When the bloom is ready (which takes trial and error to determine the right timing) you want to remove it while it's still hot and beat it to remove the remaining mostly molten impurities and consolidate it into a mostly Iron lump of metal. It usually takes multiple rounds of doing this while recycling chunks of slag Iron to produce significant quantities of reasonable quality Iron. On top of that to match the properties of Bronze tools you generally need to forge Iron, hitting it with a hammer, folding it in layers, etc. Even so, it wasn't until the middle ages that Iron based weapons were as good as or better than the best bronze weapons.

The advantage of Iron is primarily that Iron ores are ubiquitous, while high grade Copper ores are rare and Tin ores even rarer. The disadvantage is that smelting and working Iron is difficult, fiddly, and non-intuitive. Anyway, all of the above is just to say "the bridge from the Bronze Age to the Iron Age is neither direct nor straightforward". The Iron Age likely only came into full bloom (pardon the pun) due to the collapse of the Bronze Age in the Eastern Mediterranean, which destroyed the long range supply chains necessary for keeping bronze production running. The things that made Iron working accessible from the context of the Bronze Age were familiarity with all of the key ingredients: fire, heat, furnaces, transforming ores to metals, hammering metals, and so forth. Even so, it took a tremendous amount building up from those building blocks to get to a state of sophistication with Iron working of being able to produce large quantities of decent tools and weapons.

So then, of course, the question (as you've asked) arises of how a civilization might get to a state of such sophistication with Iron working without the intermediate step of Copper, bronze, etc. While the transition from Bronze to Iron was anything but direct, it did help in that they both use some similar techniques and if you have a bronze working tradition you understand the value of working metal and of iterative, inquisitive trial-and-error based exploration of how to work the material in hopes that something of value might result.

And that brings us to another important point: native metals. There's scarcely a square inch of the globe today that hasn't been picked over by generation upon generation of humans throughout history so native metals are much less common in occurrence today than they would be geologically speaking. However, various geological, geochemical, and astronomical processes result in the production of raw metals on or near the surface of the Earth. Since metals are lustrous, these are natural attention grabbers for human beings, so you can bet that ancient peoples have been glomming onto these things since time immemorial. And slowly but surely they also figured out how to work them. This form of metal working predates the full-scale form of smelting, casting, and forging that would come later in the Chalcolithic, Bronze, and Iron Ages. There's evidence of native Copper being extracted, worked, and traded in the Americas dating back some 7000 years, for example.

We have evidence of ancient Bronze Age Egyptians working meteoritic Iron, for example, as we do for pre-Columbian Native Americans. A dagger made of meteoritic Iron was found in Tutankhamun's tomb (who died well more than a century before the Bronze Age collapse). That can serve as one way into Iron-working, because it shows the value of the metal as well as makes it possible to experiment with different ways of working it without having to get everything right from the get go. If Copper and Tin (or Arsenic) hadn't been around in sufficient quantities to bootstrap metallurgy it likely would have been discovered via fiddling around with native Gold, Silver, and meteoritic Iron even so. However, it also likely would have taken much longer to proceed from there to discovering the processes of smelting Iron ore and forging Iron and steel pieces, perhaps even millenia longer. Though it likely would have happened eventually.