Augustin Mouchot developed the earliest solar powered steam engines in the 1860's, and exhibited a fairly large and developed engine at the Universal Exhibition, Paris in 1878.
Mouchot engine at the Paris Exhibition in 1878
So in terms of being possible, it was done decades before your projected time line. However, a look at the illustration tells you all you need to know why the engine wasn't adopted in 1878, the 1929's or even today.
To gather enough energy to do useful work requires a large collecting array, either a singular device, or a multiplicity of mirrors, solar panels etc. Solar energy is actually very dilute compared to chemical energy. In addition to being dilute, it is also periodic rather than "on demand", and is irregular as well, you can be defeated by clouds and rain or fog blocking the sun. Moving large mirrors, reflectors or PV panels around is inconvenient at best, and can expose you to danger (large, heavy moving parts), not to mention lots of maintenance to clean and polish surfaces, and even the possibility of losing the collector due to sudden high winds, hailstorms and so on.
In addition, there is still no clear method to store large amounts of energy for night time usage or periods of rain of clouds. This problem was already evident in 1878, and even in the 21rst century AD we still are no closer to cracking the question.
A civilization without large scale usable reserves of chemical energy (coal, wood, hydrocarbons) would then be stuck in a sort of "craft" industry economy. Solar energy would not scale to the extent required for a modern industrial economy, nor would it allow continuous production. Work could only be done essentially on sunny days, and even then a fe clouds could totally throw off production. A large steel smelter could theoretically be built with a giant solar mirror, but what would happen to the bloom if the heat is irregularly applied due to passing clouds? Other thermal processes wold also have these sorts of issues as well.
Solar furnace built at Fond-Romeu-Odeillo-Via in 1969, and still the largest in the world
So "solarpunk" could be a viable way to structure a story or setting, so long as the actual limitations of this sort of technology are acknowledged.