>Greeks did invent steam engine. They just didn't have any fuel for it except wood, and they couldn't harvest enough wood to make the whole thing practical. If the Greeks had discovered coal we might have had the industrial revolution in like 500 BC
>And the reason they did not manage to discover coal is that its is found too deep underground. It took us a long time to development the technology to be able to go that far down.
This is all wrong.
First of all, the Greeks had knowledge of coal, its properties, and other substitutes.
Second, the reason the steam engine wasn't developed until the late 17th c. and didn't become useful until James Watt was because of metallurgy, materials, and cost.
As other anons have pointed out, classical Greeks had a knowledge of steam power. The problem was they couldn't utilise it. This is because to power any machine of significant size and power, you require a few materials that the Greeks didn't have access to. Chief among these is large quantities of good quality steel (such as crucible steel), which is vital for the production of high pressure boilers, pistons, and valves, without which you can't drive anything of any real weight.
The other problem is cost. In order to build a steam engine of significant size, you will require several tons, perhaps even hundreds of tons, of iron, which all needs to be smelted and cast, which in turn requires a MASSIVE production chain involving machinery that has no purpose other than to cast huge quantities of steel, such as crucible furnaces, industrial blast furnaces, and the like.
No nation other than the Roman empire could come anywhere close to producing enough iron ore to drive this industry, and even for Rome it would be staggeringly expensive. And that's just mining the ore, next you need to smelt it, refine it, cast it, transport it etc.