[Gibbon1]

I think you are correct. Coal gave Britain a leg up as early as the 14th century but not for steel making. It's fungible though coal was being substituted for burning wood. Which means probably more wood to make steel. Also more land can be used as pasture.

Basically England was boosted by the energy input from coal.

One thing about Sweden for a long time. They had a lot of trees and very high quality iron ore. Which I think is the reason they were so powerful during that period. Sweden cut down all their trees to make steel.

When I think of steam engines I think also of simple franklin stoves and pressure cookers. People tried to make both of those long before steam engines. They are both much more efficient in terms of the amount of fuel consumed but the cost was too high for that to pencil out.