It wasn't just access to coal, it was access to coal coupled with the heat engine: heat engines used coal, but led to the production of more coal and in turn created more demand for coal. This positive feedback loop created exponential growth.

The Chinese widely used coal in metallurgy, but did not have an effective heat engine.

Romans had access to coal, even mines. That acoup article says it's the demand for coal that made the difference.

Incredible post, thanks! I'll no repeated the incorrect assertion that the Romans could have had any hope of their own industrial revolution!