Haven't read the book, but I'm a cleantech consultant with a materials science and physics background. I spend my days helping companies find and adopt and strategize around new technologies.

It's a good question and worth engaging with. I'll start by saying that, first of all, we need to consider that climate change is not an existential risk. It's a serious risk where not adapting fast enough can cause large amounts of suffering for billions of people, but it won't wipe us out or prevent the continuance of technological civilization unless we do incredibly stupid things in response to said suffering. Which is not impossible. But Earth isn't going to become Venus, or anything like that.

I'll follow that up with an observation that in the excerpts of this and the author's other books that I've found, he mostly accurately represents a number of misunderstandings and misrepresentations from the past and present of environmentalism, but he also misrepresents many aspects of the technological and economic state of competing energy sources, and of the current state of climate science. He makes some very isolated demands for rigor, like complaining about nuclear being expensive relative to fossil fuels without (AFAICT) noting that this is because it's held to a uniquely high regulatory standard way out of proportion to it's actual risks in ways that drive up construction times, financing costs, and plant engineering requirements, while preventing scale-up from letting industry grow enough to realize experience curve cost reductions and preventing plant design iterations over time. The sections I've been able to access read like someone who decided their bottom line before they decided what to write above it.

More concretely:

1. Today, in much (possibly most) of the world, kWh for kWh, solar (unsubsidized, without energy storage) is the cheapest source of electricity on the grid. This happened within the last <10 years depending on location, and I think it's important to note that Alex Epstein does not seem to have adjusted his rhetoric in response to this shift. Yes, not every market can currently afford the capex/opex tradeoff, or has the land and weather available for large scale deployment, or has a grid that can remain stable under increased intermittency, but over time these problems have been getting steadily less severe as the equipment gets cheaper, grid management gets better, natural gas use grows and gets used as peaker plants, and existing dispatchable fossil fuel capacity gets used for load following more. Today nations can credibly do things like ban building new coal plants, and there's no outcry from industry and no flight of data centers out of said country.
2. Energy storage is also getting cheaper rapidly. For lithium-ion batteries it's been on the order of 10x in the past decade, down to around $150/kWh today. This, combined with improving power and energy densities, are why we're starting to see more electric cars, and more plans by utilities to installing energy storage. I've done the math for a few models of electric and serial hybrid electric cars at current retail gasoline and electric prices, and it seems common to find that after 40-50k miles the electric car has lower total cost of ownership. For grid storage, currently most near-term plans I've seen talk about batteries on the order of 1-4 hrs of backup. That's enough to stabilize the grid to short-term fluctuations of supply and demand, improve efficiency by reducing need for spinning reserves and load following, and just generally allow each type of power plant, including fossil fuels, to be operated in the most efficient way for that plant instead of varying due to the instantaneous needs of the grid. For other types of batteries it's harder to say because they're less commercially mature, but there's been a lot of progress in areas like vanadium flow batteries, which are easier to scale to longer durations, and iron-air batteries, which are less efficient but should be much cheaper to build (making them potentially suitable for seasonal storage, where you slowly charge them whenever there's excess generation to use a few times a year.
3. Fuels. Hype about batteries and hydrogen aside, it will likely be decades before there's a truly viable alternative to hydrocarbons for many diesel and jet fuel use cases. Biofuels are pretty cost competitive these days but biomass availability is finite and probably can't sustainably scale enough to meet a large fraction of current usage, let alone future demand. E-fuels - which use electricity to capture CO2, make hydrogen from water, and turn it to hydrocarbons - are very expensive ($15-40/gallon) due to high electricity requirements and high capex. Yet we see the EU (in one of it's bold but less ridiculous moves) mandating use of sustainable aviation fuel and companies signing offtake agreements for more e-fuels than suppliers can provide. Why? Because it's a very early stage technology, and we can expect capex to fall over time like it does for anything else not unavoidably dependent on large amounts of precious metals. Because in the near term people are building plants in places where they can get nearly free electricity from trapped assets (like hydro in Norway and wind in West Texas). And because by the time it does need to scale up, that electricity is going to be coming from renewables, and peple are going to be building plants wherever renewables are cheapest. That means (even with current solar power tech) <$0.02/kWh, compared to a global average of around $0.19 today for the grid as a whole. That's why we see Australia announcing a 50GW solar power project to be built in the outback by 2030 to make hydrogen, ammonia, and methanol for export.
4. In the long run, that which is not sustainable will not be sustained. Global fossil fuel use will eventually end, and we're lucky humans are in a position to decide how to do that on our own terms. An abrupt end would genuinely be terrible. A decision 30 years ago to phase fossil fuels out by today would genuinely have left humans with no viable replacement that could have been cost-effectively scaled up in time. That's no longer the situation we're in. We've solved many of the problems technologically, and some of them economically. We can see the shape of both the major remaining problems and of multiple solutions forming for each of them that can feasibly be ready by the time we need them.

If Epstein’s thesis is, broadly, “cheap energy from fossil fuels is awesome and climate change isn’t that bad”, weaknesses would be likely to fall somewhere under these, classified in increasing controversy:

• Climate change might be worse than he’s positing. Particularly, climate is a global system we only partly understand, and our error bars for the effects of inadvertently perturbing it may be quite large
• Cheap energy may be obtainable from non-fossil sources. Epstein is keen on nuclear energy (why?), but, as AnthonyC points out, solar & wind are getting surprisingly cheap (for example https://www.bloomberg.com/news/articles/2021-06-23/building-new-renewables-cheaper-than-running-fossil-fuel-plants). Obviously that only gives you a bonanza of cheap energy when the wind blows and the sun shines, but “the sometimes-free-energy bonanza will destabilise the grid!” feels a long way from common-sense
• GDP may be possible to decouple from energy use by purely technical means: compare the computation-per-watt-hour of a Pentium with that of an iPad. Compare a Passive-House-standard building with an average building. How far are we from the optimal frontier? There will be, at some point, a limit, because we’re operating with optimal designs and can’t get any better, but we might be quite far from that point - countries with more energy-tight housing often have codes that require that, rather than the market doing it spontaneously? Why is that? Principal-agent problems? “Market for lemons” informational issues?
• GDP may be possible to decouple even further from emissions use via selective lifestyle changes (higher-density cities, more bicycles, fewer automobiles)
• GDP may be argued to be decouple-able from human welfare. Broadly, this is the “degrowth” argument. Critique here, for example  (https://www.noahpinion.blog/p/people-are-realizing-that-degrowth)