It Would Take The Atomic Age to Make Us Skip Fossil Fuels
Exactly as you said: A breakthrough in technology that made renewable energy cheaper than the oil bubbling out of our back yards. Remember that the internal combustion engine didn’t come along until the 20th century. Fossil fuels killed the electric car by being cheaper. If Martin Klaproth went further with his experiments with Uranium, we would never need petroleum.
Holland had an incredible economy based only on their famous windmills. They drained swamps, milled lumber, processed grain and food, irrigated fields and did almost all civil activity by windmill. But they did have the advantage of steady and reliable wind energy. The rest of the planet isn’t so lucky; that’s a regional thing.
History: Electric cars
In 1821 Michael Faraday created the first rotating electric motor. Less than a decade later the world was in their back yards strapping these to carts and contraptions trying to move around with them. As early as the 1830s, inventors in Hungary, the Netherlands, the UK, and the US were focusing their efforts on combining these technological advances to create a powered motor vehicle. Batteries were the problem: they were made by mixing chemicals in jars. In the 1860s, a French physicist by the name of Gaston Plante invented the first rechargeable lead-acid battery—a huge breakthrough for electric mobility. This is the time the Studebaker brothers immigrated to America and began their coach-building empire. They had always had their eyes on electric motors, hoping one day to perfect a motorized coach. Finally, in 1901 Studebaker began selling battery electric cars amongst some heavy competition.
(1911 Babcock Electric Co. Model 12 Roadster)
But batteries never got lighter. Charging them never got faster. They never got the power of exploding naphtha. Petroleum put dollars in our pockets and we fell in love with the cheap, powerful, convenient gasoline engine.
Studebaker shut down their electric car line in 1911 and began making gasoline cars.
Portability is the key
Gasoline is so easy to carry around, we can’t justify anything else. Wind power is great for Holland, but how do you carry it to Nevada? Solar power is awesome in New Mexico, but how do you box it up and use it in Montreal? Tidal energy is amazing if you’re in the Bay of Fundy, but what good is it to people in the Sahara? Make your electricity portable.
We have Portable Electricity
An electric world needs electricity. We can make an incredible amount of safe electricity anywhere we want today, in any climate and on any terrain, on the land, in the sea, and even on the moon.
It’s called Nuclear Power. In 1954, the Navy launched the first submarine that used radioactive material as a power source. Its name was the USS Nautilus and it was the first submarine to travel to the North Pole in 1958. Before then, submarines used diesel engines and had to go into port for fuel. Nuclear power allowed submarines to run for about twenty years without needing to refuel. Over 160 ships are powered by more than 200 small nuclear reactors today. The Seawolf class submarines originally built 25 years ago have never refueled, and they never will need to refuel.
(A field full of 20mW Vesta wind turbines which will cover 101 square kilometers of farmland)
While it requires 100 massive wind turbines covering 25,000 acres (101.1 Km$^2$) to provide the brand new Courtenay Wind Farm's 200 megaWatts of power (above), The Virginia-class attack submarines were the first to have a core reactor designed to last the 33-year life of the vessel. It delivers 230 MegaWatts, and fits easily in the 33-foot diameter hull *(below).
(A 210mW power plant running in a 37 square meter room on a ship. It will never refuel.)
The US Navy hopes to have the first replacement for the Ohio-class ballistic missile submarine on duty by 2031. When that vessel is launched, the onboard nuclear power plant is expected to last its entire 40-year service life.
It is a steam engine
The power creates almost no carbon emissions. Nothing is burned, there is no exhaust. A nuclear reactor is nothing more than a heat engine; the same engine we fell in love with in the 18th century.
If we had the power of the atom in 1860’s we would have laughed at the drilling and mining and refining required to support the combustion engine, and there would have been affordable, small nuclear plants in every single town. All the sources we talk about today - wind, solar, petroleum, coal, hydroelectric - are only good on earth. When we leave earth, nuclear power will be our only option.