You need to be careful about what you mean by "steam engine time."
The link you gave has different interpretations. Gibson said "there was nothing technically stopping the Romans from building big steam engines" while the commenter says "The Romans had the idea of steam engines, but not of strong iron to contain the pressure, nor valves to regulate it, nor the cheap fuel to power it."
You apparently disagree with Gibson's characterization.
The original 1931 claim gives a third; "A social growth cannot find out the use of steam engines, until comes steam-engine-time"
However, As Anton Howes (co-author of the linked-to page) argues at https://www.ageofinvention.xyz/p/age-of-invention-why-wasnt-... , steam engines came decades after the pieces were available, and well after initial uses (like pumping water from a mine) were conceived of, and where there would have been social growth had they been available:
> So why did it then take almost another half a century, even with the increasingly widespread understanding of atmospheric pressure and vacuums, for a widely-adopted and practical atmospheric engine like Thomas Savery’s to appear?
> The answer, I think, is what it almost always is: that inventors are simply extremely rare. People can have all the incentives, all the materials, all the mechanical skills, and even all the right general notions of how things work. As we’ve seen, even Savery himself was apparently inspired by the same ancient experiment as everyone else who worked on thermometers, weather-glasses, egg incubators, solar-activated fountains, and perpetual motion machines. But because people so rarely try to improve or invent things, the low-hanging fruit can be left on the tree for decades or even centuries.
> The development of the steam engine, rather than being a story of the Torricellian vacuum science unlocking a new technology, is instead just like that of textile machinery, signalling systems, and any number of other “ideas behind their time.” The rate at which such inventions appear is really down to the number of people applying themselves to improvement, and the strange-seeming delays are down to there so often being so few. When only a handful of people are inventors, is it really any wonder that the circumstantial setbacks and distractions that prevented a Petty or a Kalthoff can end up delaying things for decades?