The problem I see in your question is understating how much of human technological development was based on fossil fuels.
I mean you need coal to get from Bronze age to Iron age
To skip from bronze to ... I guess an Atomic era would be a tremendous leap.
But lets give our selves a chance, and limit your scenario to
What would it have taken for the world to skip fossil fuel based power stations?
What do you say? is this acceptable?
If yes, than the answer may be just a small change in perception, first coal based powerplant was commissioned by none other than <PERSON> a Edison Electric Light Station in 1982 this allowed for electrification of London using DC current. And there was little to no choice, because DC is annoyingly hard to transfer over long distances, you need your Power Station to be within a kilometer I think for the DC Station to be effective. The transfer over long distances, would be later facilitated by AC current, its efficiency further improved using 3-phase AC.
Since the 3-phase AC could be transferred over almost any distance it made sense to use water as the source of the energy for electricity generation, in fact both the first commercial installation Lauffen Power Station in 1892 which transferred the AC current to over 109miles distant Frankfurt, Redlands Power Station (1893), Folsom Power Plant(1895) and famous Tesla Westinghouse Niagara Fall Hydro-Electric Power Station(1895) all used a hydroelectric principle.
It was only later the higher efficiency steam generators/alternators became the primary source of electricity. The acceptance was high because, well for past 13 years coal plants have been used to generate electricity, so what's the problem, just replace the dc generators with alternator.
The point of diversion however is: what if construction of coal based DC power station coincided with the hydroelectric AC powers stations.
I expect that one aspect, the Westinghouse would harp on to promote his AC alternators, would be the quality of air consideration. 284
It would be very easy to point to black lung, the noise, the soot all over, comparing the Niagara fall's clean and CHEAP electricity with coal based station in the middle of the city, would be very easy. Since the AC also just happens to be easier to transfer, it could give a death blow not only to DC in the current war, but also to fossil fuels as a primary source of electric energy.
This could in turn start the renaissance of clean energy generation. Hydroelectric, wind, coastal. All this would be used, the coal plants would be used only when no suitable source would be near by, and effort would be made to get rid of it. The suitable alternatives would later become Nuclear and Solar, but that is way down the line.
At the same time, large effort would be given to electricity storing.
You don't really need any technological breakthrough, only make the fossil fuels seem unappealing at exactly the right time, and the gradual technological improvements will take care of the rest. 778