Q:

What is the best way to implement the top solution to climate change politically?

Please don't answer without citing scientific research which has a general consensus or article from a reputable source based on verifiable research citations.
I recently read this article about a 2017 PNAS study from Griscom et al (link below) that "estimated natural carbon solutions (NCS) (essentially ecosystem regeneration) have the potential to provide up to 37 percent of the CO2 mitigation that we'd need through 2030, for a 66 percent chance of holding warming to below 2°C."
Most geoengineering solutions have significant risks or unknowns which greatly reduce their benefit. Reducing fossil fuel use immediately will reduce short-term economic output with replacing with renewables and alternatives. Maybe simply paying drivers incentives to use alternative vehicles is most-cost effective, as transportation is the largest percentage of greenhouse gas emissions in the US (EPA). 
Global energy-related CO2 emissions were 33.1 Gt CO2 in 2018 according the [IEA report][6]. Apparently from the Griscom study, $10 USD MgCO2e−1 is the "current cost of emission reduction efforts underway and current prices on existing carbon markets" from 2017. Our CO2 emissions cost us 10 billion USD per year. For reference, global GDP is at US$84.84 trillion for 2018, meaning reducing our entire emissions to zero would cost 0.0001% of global GDP.
Griscom et al, https://www.pnas.org/content/114/44/11645
EDIT: I've moved the physical science question about which current solution is the best to EarthScience.SE, and reworded the political question here which is how to implement the best solution known by science? While the answer might vary by a particular solution, in general, a given solution can be seen to cost x amount of dollars and will take political will to achieve, whether by governmental or non-governmental means. So then how do various political strategies compare and are some better fit for mitigating climate change?

A:

I don't see how this is anything other than an opinion fest ultimately. Just consider this BBC news piece

Researchers say an area the size of the US is available for planting trees around the world, and this could have a dramatic impact on climate change.
The study shows that the space available for trees is far greater than previously thought, and would reduce CO2 in the atmosphere by 25%.
The authors say that this is the most effective climate change solution available to the world right now.
But other researchers say the new study is "too good to be true".
The ability of trees to soak up carbon dioxide has long made them a valuable weapon in the fight against rising temperatures.
The Intergovernmental Panel on Climate Change (IPCC) said that if the world wanted to limit the rise to 1.5C by 2050, an extra 1bn hectares (2.4bn acres) of trees would be needed.
The problem has been that accurate estimates of just how many trees the world can support have been hard to come by.

The same issue of the difficulty to estimate costs probably applies to almost every solution proposed.
Also

The study has been published in the journal Science.

So this is not riff-raff, but top-level science. Which doesn't make it bullet proof.
Perhaps a more sobering paper:

The long-term economics of mitigating climate change over the long run has played a high profile role in the most important analyses of climate change in the last decade, namely the Stern Report and the IPCC's Fourth Assessment. However, the various kinds of uncertainties that affect these economic results raise serious questions about whether or not the net costs and benefits of mitigating climate change over periods as long as 50 to 100 years can be known to such a level of accuracy that they should be reported to policymakers and the public. This paper provides a detailed analysis of the derivation of these estimates of the long-term economic costs and benefits of mitigation. It particularly focuses on the role of technological change, especially for energy efficiency technologies, in making the net economic results of mitigating climate change unknowable over the long run.
Because of these serious technical problems, policymakers should not base climate change mitigation policy on the estimated net economic impacts computed by integrated assessment models. Rather, mitigation policies must be forcefully implemented anyway given the actual physical climate change crisis, in spite of the many uncertainties involved in trying to predict the net economics of doing so.

Also there are quite a few more papers/discussion on https://en.wikipedia.org/wiki/Economics_of_climate_change_mitigation#Assessing_costs_and_benefits
And if you ask an economist:

What is the most economically efficient way to reduce greenhouse gas emissions? The
principles of economics deliver a crisp answer: reduce emissions to the point that the marginal
benefits of the reduction equal its marginal costs. This answer can be implemented by a
Pigouvian tax, for example a carbon tax where the tax rate is the marginal benefit of the
emissions reduction or, equivalently, the monetized damages from emitting an additional ton of
carbon dioxide (CO2). The carbon externality will then be internalized and the market will find
cost-effective ways to reduce emissions up to the amount of the carbon tax.
However, most countries, including the United States, do not place an economy-wide tax
on carbon, and instead have an array of greenhouse gas mitigation policies that provide subsidies
or restrictions typically aimed at specific technologies or sectors.

The rest of the paper goes on dozens of pages discussing these second-best solutions. I've read the conclusion section of the paper too, but other than saying that static cost estimates are probably unsatisfactory, i.e. we need to somehow estimate how much new technology is going to cost... there's no deep conclusion there. (Ok they do say that even for static costs of many programs, the complicated structure of semi-hidden subsidies makes the analysys not always straightforward.)

