We've already innovated our way out of this mess. We have all the technology available now to decarbonise the economy (well, mostly; we're still a bit limited in a few areas; but we can get a lot of the way there).
Covid is a good example. In most of the liberal democracies people accepted the restrictions their governments argued were necessary to combat Covid. I think these restrictions were significantly greater than what is needed from individuals to combat climate change.