I am confident that industrialization is possible without fossil fuels, however it’s quite improbable without magically making them disappear. Fossil fuels have a high energy return on investment (EROI). You are probably familiar with the fact that for most of human civilization, the vast majority were farmers that produced some surplus so that other humans could specialize in other professions. EROI describes a similar phenomenon. Whereas in Colonial America, 90% of people farmed to support the other 10% of the population, in Modern Civilization, something like 10% of the economy goes to producing energy required for the other 90%. EROI specifically is a ratio of the following:

The following are the EROI of various energy sources according to Energy and the Wealth of Nations: Understanding the Biophysical Economy:

Higher EROI is better, and indeed necessary for various ways of life. For modern civilization, I think our EROI is 10:1 (or maybe that is just America specifically). The book argues that from 1560 to 1720, Sweden was a great power with productive mines that relied on abundant energy in the form of charcoal. The EROI on this biomass was 4:1 until the woods were over-harvested in the mid 19th century. Since then, mass migration followed along with the decline of Sweden relative to its peers. If the EROI is lower than 3, it is basically useless.

With that out of the way, let us consider various sources of non-fossil power, their benefits, and their drawbacks.

• Hydropower - This actually dominated the Industrial Revolution in Britain in the 18th century. Today, the energy produced from hydroelectricity is equivalent to the energy consumed from coal in 1890. There are obviously some untapped sources but I am not sure what the total is. Wind mills have an efficiency of less than 60%, while turbines have an efficiency of 95%. While some turbine designs were developed before the Industrial Revolution, modern designs came after hydropower was displaced by steam engines. Water wheels are also disadvantageous to the bourgeoisie - steam engines can go anywhere, but a water wheel cannot. Electrification provides a solution, but it requires high capital investment and an invention of the mid 19th century.
• Wind power - Also something used in real life. Unfortunately, the industrialist does not like being told by nature when work must start and stop. Modern wind turbine design is a 20th century invention, although you can still get some decent power out of older designs. You can also go surprisingly big just with wood. In real life, they had trouble competing with cheap fossil fuels.
• Concentrated solar - A solarpunk 19th century?! The first solar thermal engine was developed in 1897, and the first solar thermal power plant in 1912. Concentrated solar power can also be used for very high temperature furnaces. They probably could have been developed earlier. However, one study suggests its EROI is a measly 1.6. I am not sure why.
• Biomass - Burning wood basically. See the Sweden example for why this is an issue. Also, the Industrial Revolution’s use of coal and the development of the steam engine is directly related to Britain running out of wood. If you look at this graph, you will see that relative to other sources, traditional biomass as a source of energy has barely grown in the past 200 years. There’s just not much room for growth.
• Biofuel - Oh boy. Biofuel ranges from barely usable to literally useless. This study states “EROIs for bioethanol were: 1.797 for sugarcane, 1.040 for corn, and 0.739 for wood. The results for biodiesel were: 3.052 for African palm, 2.743 for pinion, 2.187 for bovine fat, and 2.891 for swine fat.” So the best biofuels have an EROI similar to biomass from the Sweden example, but require complicated processing and probably can’t even be used to make steel. The only biofuel with good EROI is algae which will require genetic engineering - useless for this exercise. If you want biofuel to play a role in fictional industrialization, you will have to introduce fictional organisms.
• Photovoltaic - Surprisingly, these were invented by George Cove in 1905 before the mechanism for how they worked was discovered lol. The low-tech ones have really bad efficiency though.
• Nuclear fission - Maybe with a lot of dumb luck and death by radiation you could get one built earlier…

So it’s quite obvious that this alternate timeline will have to rely on hydropower. It works fine for textile factories, which is what the First Industrial Revolution was all about anyway. Really, you need to stunt the development of the steam engine. In England, they didn’t have enough wood, so they started mining more coal. The coal mines would be flooded with water, so they needed to pump it out. The invention of necessity was the steam engine - it used the coal and water already there to pump out the water. If the country doesn’t run out of wood, that would delay the engine a bit (although the population will continue to grow, so I’m not sure if this could last). If the country simply didn’t have much coal, that would be even better for hydropower. While steam engine development will be slow, water turbines will probably get developed much faster.

However, there are some issues. Steel production was THE thing in the Second Industrial Revolution, and I am pretty sure that will require coal coke. Direct reduction with hydrogen requires a lot less coal, but it’s way more expensive and requires modern arc furnaces. Also, by delaying the steam engine, you are doing a terrible thing - creating a world without trains. Or perhaps pneumatic trains would be developed instead?

When electricity is discovered, electrification will probably proceed relatively quickly as it will be even more transformative. In this coal-poor, hydro-rich country, electrification would be great for transportation. Pneumatic trains cannot go far, steam locomotives are probably underdeveloped in this timeline and rely on imported coal or expensive domestic wood, and maybe there’s a couple fireless locomotives that run off of steam produced by a solar thermal power plant. The flexibility of electricity will be a great boon to the bourgeoisie - something they missed in this timeline’s 18th century when the steam engine was not developed. The state will probably start constructing gigantic hydroelectric plants as well.

OK it’s literally 2:00 AM at this point and I have been working on this for hours so I am just going to finish this with some rambling. Here are a couple socialist scenarios for preventing climate change. If lots of socialist revolutions happen between 1850-1900, the planet is probably fine. Marx was talking about the metabolic rift and there was conjecture about greenhouse gases as early as 1912. Global energy consumption didn’t explode until 1950, so plenty of time for socialist governments to do something. Also, if the Diggers somehow won the English Civil War and other peasant movements won in continental Europe, you might’ve had some weird not-capitalism kinda-socialism industrialization… it’s an under-explored topic in Alt History in my opinion.