The Industrial Revolution was not built on the steam engine alone.

The early steam engines were extremely inefficient, using oxen to move pumps was more economically sound. The only situation in which an early steam engine was useful was if you had tons of cheap combustible material available, that is at a coal mine. Coal was only being mined because woods had basically disappeared in early modern Western Europe (and china), so who could used coal. Europeans had also been tinkering with mechanical instrument for fun for centuries (early mechanical clocks were not better than sun clocks, but were built only as a show of wealth, plus the early modern passion for weird machines and, usually fake, automata). Gunpowder had also forced European metallurgist to learn how to make precise cylinders able to withstand high pressure. By comparison the Roman lacked: * need for coal, as olive oil and oil production waste was largely used as an alternative and cheap source of heat. * No idea of how to build pressure resistant cylinders * Not a lot of interest in machines.

The most important difference is the British built a political/economical system where if an aristocrat wanted to make more money they needed to innovate and invest, because workforce was limited and free to do whatever they want. A roman aristocrat could always just buy more slaves.

Assuming it is about Steam engine being invented during Roman times, not to mention they had slaves for doing literally everything

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