Or your example, how would we have processed ore into metal without coal (on any significant scale).
We have been processing ore into metal with coal for thousands of years. It sounds like you are arguing that the industrial revolution has been happening for thousands of years. Which it has not.
We also made bread in the industrial revolution which is needed to feed the workers. Without feeding the workforce we could not access certain advancements. Is bread a corner stone technology of the industrial revolution? No it is not. It in no way defines what the industrial revolution was. Just like coal or oil.
You can run a steam engine off of coal, wood, oil, nuclear, basically anything that creates a lot of heat. Coal is more convenient in a lot of ways but it did not unlock anything special. If not for coal we could use wood or charcoal. That was the steam engine, not the fuel it runs on.
And if the advancements were because of these fuels that why did it not happen 1000s of years ago when we had access to them?