There isn't just one story here, but several, and it's mostly pre-historical (so at the edges of suitability for this sub), but there are a lot of commonalities to the stories.

It seems to be the case that all metalworking traditions start with native metal. Native metal is raw, mostly elemental metal that occurs naturally. Sometimes it can be on the surface in large pieces, sometimes it can be in tiny bits and flecks mixed in with other material. Some familiar examples of native metal are meteoric iron and native gold (in the form of nuggets or flakes/dust in alluvial deposits). Starting with native metal jump starts the whole process, especially from a discovery standpoint, because you begin with something that is already interesting and something that is already in a state where exploring its physical properties and how it's worked is an easy and natural step.

One mistake that is easily and often made is thinking that the "natural" world as it exists today is identical to the natural world as it existed in the past, even the distant past. This is, of course, not true, due to a variety of factors, but most prevalent among them is human activity. When we go out into the wilderness we like to tell ourselves we're experiencing raw, untouched nature. But the reality is that there's scarcely a square centimeter of either the "New World" or the old that hasn't been seen by human eyes and disturbed by human hands. That has no doubt resulted in a massive depletion of native metals, especially gold, silver, and copper, so what we see today (even in "nature") does not represent their actual abundance as a resource for stone age peoples.

The "easiest" native metals (gold, silver, and copper) are also fairly easy to work. They are fairly soft so can be pressed or hammered into different shapes and forms, even with stone, wood, or bone tools. They all are also amenable to melting and casting, and this can be done even with just a fairly hot "campfire", without necessarily requiring extremely specialty built furnace equipment. Given humans had mastered fire early in the stone age it was really only a matter of time before someone who was intrigued by a bit of native metal decided to try heating it up and discovered that it could melt.

There is evidence of metalworking traditions relying on native metals (including mining native metals) going back many thousands of years. In North America working and mining native copper dates back to 6000 BCE, at least.

On top of that, mining and smelting ores is actually something that can easily happen accidentally, particularly with metals like copper and tin (unlike copper, tin does not occur as a native metal at all). Many copper ores are strikingly colored or interestingly textured (malachite, cuprite, chalcopyrite, azurite, etc.), as are tin ores (such as cassiterite), and lead ores (galena). Precisely the sort of thing that would draw the attention of a human and encourage them to collect, investigate, and hold onto. And smelting those particular metals requires exposing them to reducing conditions at high enough temperatures to reduce them from their oxidized ore states and melt them, separating them from impurities in their ore bodies (such as silicates). Now, you may ask, where is a stone age person going to get a reducing agent? Well, this is quite simple, as carbon monoxide is a very effective reducing agent.

Inside of many perfectly ordinary campfires are the conditions necessary to smelt galena into lead metal, and, of course, the same fires can be used to melt and cast lead after it has been smelted. There is evidence of lead smelting and casting at Catal Huyuk dating back to 6500 BCE. Once that door has been opened to you it becomes a simple matter of trial and error to improve the process and adapt it to other materials (such as copper and tin ores). Improvement in this case means improving the reducing atmosphere within the fire, which is easily done by adding an excess of charcoal (a practice which dates back at least to 3700 BCE) and increasing the temperature of the fire, typically by blowing air through pipes into it. With just that you can smelt and cast lead, copper, and tin (and a few other things), and that sets you up for a magnificent process of iterative experimentation.

The main constraint on bronze metalworking is availability of materials. Copper ore is fairly rare and tin ore even rarer. So it took a while for long range trade of tin and copper (across entire continents) to ramp up before the use of bronze could be competitive to the use of stone for tools and weapons. That's a major reason why it took thousands of years to transition from the earliest metalworking (and mining and smelting) to the era of the bronze age where bronze materials were actually supplanting stone on a large scale and for practical (rather than ceremonial, decorative, or status symbol) uses.