Replacing high CO2 intensity activities (burning coal) with lesser intensive tasks (e.g. burning gas or renewables) is the key.
Solar and other renewables counteract their Co2 expenditure after 1-2 years.
It will be necessary to lower demand for fossil fuel enough that new prospecting becomes unprofitable. This will happen eventually due to the physics of oil drilling.
If you consider the amount of energy contributed to the world economy from fossil fuels, there is no clear path how to market alternatives in quantities that can make fossil fuels obsolete.
A more realistic scenario for around 2050 is that coal-power increases while oil for personal transportation is replaced by batteries due to high oil price.
Of course you need to spend money and energy (specially energy, everything in the universe is energy), but the solution is not to stop moving. We need to use energy and resources in order to switch to better technologies.
GDP measures the total production of an economy. That is mostly equivalent to energy_consumption * p_efficiency.
Investing in new technologies that increase efficiency has always been a good decision. Maybe you can improve solar panels by a further 5% and batteries by 10%?
Realistically, energy_consumption will need to decrease, but that isn't actually that terrible.
Again, GDP measures how much money is spent within a country, if there are several intermediaries in a supply chain, the cost of products and services increases and the GDP tends to rise.
If a country change direction and leans towards nuclear energy, the GDP (that is in fact a terrible measure) will increase cause the new expenditures.
Assuming there is validity to the numbers (and no new source of energy), it means you need to reduce GDP by 2-5% yearly until 2050. But GDP and money is a "sliding" scale so it might mean something different by next year.