Go someplace with abundant resources. Keep your population small. Avoid the living hell of early agriculture.
The Newcomen and later Watt engines were enormous fixed engines that operated at extremely low efficiency, low operating speed or reciprocation frequency, and very low power output, primarily used for light pumping or blowing operations. It was in no way usable for transportation or effective electricity production. And the 125 psi rating stated above was for small fittings; for large pressure vessels (which, again, would require threaded fasteners and tensile-compressive spring joints) the allowable pressures are likely quite low, as in the teens or less, for any credible wall thickness.
This is fine if you intend to keep the population small and mobile, but as I’m sure you are aware, hunter-gatherers were typically semi-nomadic, moving with the change of seasons or depletion of local resources, and had a number of different methods for maintaining population at tribal size at a manageable level to afford the support of available resources. Hunter-gathers not infrequently suffered famine, often wiping out entire communities. There is no mechanism for hunter-gatherers to develop advanced industry or the intensive materials resource extraction base to support it, so technology is limited to the materials and resources that are readily at hand (wood, natural fiber, bone, skin/fur, and stone). There is much to be said for the general quality of life of the hunter-gatherer lifestyle in a resource-available environment, especially in comparison to the backbreaking serfdom of early agricultural societies, but it isn’t going to lead back to an industrial capability.
Stranger
And that’s not a problem because a Newcomen engine wouldn’t be used to generate electricity. It would be used to pump water out of the tin, coal, and iron ore mines so you could build more serious stuff. You know, just like in the 1700s.
The Long Earth by Pratchett and Baxter is based on a quite similar scenario - humans discover the ability to “step” to (initially) uninhabited parallel versions of Earth. However it differs from the OP’s scenario in that the steppers can carry material with them, with the exception of objects made of iron.
How does that accelerate the progress of industrialization? Setting aside the necessity of locating mineral deposits to mine, there is still the need to recreate the precursor technologies to modern industrialization, which necessitates having an adequate food production base such that the population is not living on subsistence agriculture, et cetera.
There are very few technologial innovations that just came out of nowhere that created revolutionary advances in technology and industry; most awaited sufficient resources (labor, energy, or materials) to implement previously ideated concepts. Without bringing along examples or people directly experienced in the application of those primitive levels of creating the implements and precursors of industry, you’re left with essentially the same path and time to recreate these processes. Textbooks and referneces are no substitute for the actual experience, and many details of the application of primitive technologies such as flint knapping, Hellenistic glass production, and early methods of improving steel properties prior to the ability to create refined alloy materials and smelting with high temperature blast furnaces (which required enormous amounts of charcoal or coal, mined by legions of dedicated workers under essentially slave-like conditions) are poorly documented at best.
Any technology that could not be reproduced from readily abailable materials within the lifetimes of the original settlers, or at most their immediate progeny, would be essentially lost into legend, at best recognized as such after being recreated. And expecting even a technologically knowledgeable population to go from sticks and stones to internal combustion engines and steel metallurgy, much less power plants and microchips within a century is hopelessly optimistic.
Stranger
This is the case for H/Gs that exist in parallel with, and marginalized by, agriculturalists. It’s not been shown to be the case for H/Gs that have no competition for the best lands.
And I can, anyway, think of two big exceptions - the Pacific North-West First Nations and the pre-agriculture Natufian culture of the Levant both developed permanent settlements while still H/G cultures (You may have heard of a town called Jericho? H/Gs first lived there).
PNW Natives used copper. Iron is, in fact, much more ubiquitous than copper+tin, and relatively easy to smelt to steel if you retain the knowledge of the processes required.