How long has science known about CO2-induced climate change, and are we clever enough today to geo-engineer our way out of cooking ourselves to extinction?
In brief: a long time, and most likely no.
Clive Thompson has written engagingly about the 19th century scientists — Joseph Fourier (1768-1830), Eunice Newton Foote (1819-1888), John Tyndall (1820-1893), Svante Arrhenius (1859-1927), Arvid Högbom (1857-1940), and Samuel Pierpont Langley (1834-1906) — whose work in aggregate pieced together the essential facts about CO2-induced global warming. 
In 1856 Eunice Newton Foote, an American woman, suffragette and amateur scientist, conducted the first known experiment in CO2-induced climate change science, which proved carbon dioxide and water vapor were radiant-heat trapping and retaining gases, and not thermally transparent as generally believed. In the scientific paper she submitted to the American Association for the Advancement of Science (which had to be presented by a man) she prophetically observed: “An atmosphere of that gas would give to our earth a high temperature.”
Between 1859 and 1860 Irish physicist John Tyndall conducted many elaborate experiments that confirmed Eunice Newton Foote’s results with great precision (without acknowledging her, whether intentionally or out of ignorance is unknown). He found that CO2 could trap 1,000 times as much heat (infrared radiation) as dry air.
In 1896, after an arduous yearlong effort, Swedish scientist Svante Arrhenius created the first model of CO2-induced climate change, aided theoretically by geologist Arvid Högbom’s findings on the carbon cycle, and aided experimentally by Samuel Pierpont Langley’s thermal detector invention.
Quoting from Clive Thompson’s article:
When [Arrhenius] was done, he made a striking prediction: If you doubled the amount of CO2 in the atmosphere, it would raise the world’s temperature by 5 to 6 degrees Celsius. Remarkably, that analysis holds up pretty well today, even in an age where climate analysis involves far more information and variables and are crunched by cloud supercomputers. Despite having done his work by hand, using data that even he regarded as woefully inadequate, Arrhenius reached “a conclusion that millions of dollars worth of research over the ensuing century hardly changed at all,” as Isabel Hilton wrote in 2008. The era of modern climate modeling was born. …[Arrhenius] expected it would take 3,000 years — fully 30 centuries — for CO2 levels in the atmosphere rise by 50%. Instead, [they] shot up by 30% in only one century.
In the century since Arrhenius (the 20th century), the scientific awareness of CO2-induced global warming skipped along to Guy Stewart Callendar in 1938, Hans Seuss in 1955, Roger Revelle in 1957, the computational three-dimensional Global Climate Model by Syukuro Manabe and Richard T. Wetherald in 1975 (where doubling CO2 in the model’s atmosphere gave a roughly 2°C rise in global temperature), and then to James E. Hansen’s striking Congressional testimony in 1988 that changes in the atmosphere due to human pollution “represent a major threat to international security and are already having harmful consequences over many parts of the globe.” 
The Intergovernmental Panel on Climate Change (IPCC) of the United Nations was established in 1988, and since them we have all known or denied the truth of the matter, to variously fret gloomily or agitate frantically over it, and to governmentally ignore responding usefully to it.
Well, our food, wealth, comfort, entertainment and daydreams are all disgorged (or destroyed if you’re among the sacrificed) by fossil-fueled capitalism, so cook ourselves we must because we can’t bring ourselves to trim any of those economically fungible desirables. Can our clever technologists geo-engineer an atmospheric CO2 retrieval and sequestration technique? Today, many such ideas are being proposed and explored experimentally, which their promoters hope if developed successfully into patented salvations will shower them ceaselessly with torrents of gold.
One such project that has shown technical feasibility is the Carbfix Project in Iceland, where CO2 gas is mixed into and retained by a large quantity of water (salt or fresh) that is then injected under pressure deep underground (800 to 2000 meters) into formations of vesicular or porous basalt rock. Basalt is a mafic extrusive igneous rock formed from the rapid cooling of magnesium-rich and iron-rich lava exposed at or very near the surface of a terrestrial planet or a moon; for example at spreading centers between tectonic plates. Iceland sits athwart the Mid-Atlantic Spreading Center and is an island mountain of volcanic and geothermal activity. The Carbfix scientists and engineers have demonstrated the petrification of aqueous CO2 into carbonate rock nodules within basalt vesicles (pores). Basalt does not wash away under pressurized aqueous injection, as softer sedimentary rocks do, and the metals in basalt are needed to react with the carbonated water (ideally the CO2-water mixture having been pushed entirely into carbonic acid) to petrify it. 
The pumping of CO2 into deep basalt formations, for petrified sequestration, has been known scientifically since 1976 (first proposed by Italian physicist Cesare Marchetti) , . In 2012, as a satirical hypothetical example of fossil-fueled fanaticism, I proposed that the United States capture all the CO2 released by burning the expected liquid fuel to be processed out of the Athabasca Oil Sands of Alberta, Canada (to be imported to the U.S. via the proposed Keystone Pipeline), by piping that CO2 300 kilometers (186 miles) west of the Oregon coast into the Pacific Ocean and then under extreme pressure down 2,700 meters (8,900 feet) into the basalt formations of the Juan de Fuca tectonic plate. 
The difficulty with any carbon sequestration technique is demonstrating that it has a positive Energy Return On Energy Invested (EROEI).
Basically, is the amount of energy expended per unit mass of CO2 sequestered (the energy to capture, store, transport, pump and contain the CO2 underground) LESS THAN the energy liberated (with perhaps only 30% of it converted to useful work — mechanical/electrical energy/power/torque) from the combustion of whatever amount of fossil fuel produces that same unit mass of CO2?
If not (which has always been the case so far) then it is MORE EFFICIENT, and LESS CO2 releasing to- and accumulating in- the atmosphere, to not burn the fossil fuel in the first place. Consequently, it would be unnecessary to bother with the proposed geo-engineering scheme of CO2 retrieval and sequestration.
But even if such a sequestration scheme has a negative EROEI, wouldn’t it at least slow the overall rate of CO2 emissions from our fossil-fueled civilization?, and so slow the ever-increasing rate of global warming?
A better investment of the energy required for negative EROEI sequestration schemes would be to apply that fossil fuel-derived energy to the construction of reliable (well-known, old in concept advanced in construction) robust for the long-term ‘green’ energy technologies that REPLACE (not add to) an equivalent capacity (in Watts) of existing fossil-fueled power-generating and power-using infrastructure: a fossil-fueled conversion to a green energy future. This in fact is the only realistic and practical Green New Deal (GND) that we could have. We are locked into cooking ourselves disastrously but we could do it at a slower rate — and that is what a real GND would be.
To my mind the fact that terrible climatic things are unavoidably scheduled to happen does not mean that we — humanity — are physically helpless to prevent the worst of all possible fates, by vigorously responding with intelligent and cooperative social adaptations (lifestyle simplification and energy efficiency) and clever engineering for an ongoing and permanent transition from fossil fuels to green energy.
The state of the natural world is a mirror to our civilization in the same way that Dorian Gray’s poisonously false beauty was reflected by his hideously magical portrait picture.
Thanks to Katje Erickson for pointing me to items  and .
 How 19th Century Scientists Predicted Global Warming by Clive Thompson (Today’s headlines make climate change seem like a recent discovery. But Eunice Newton Foote and others have been piecing it together for centuries.) 17 December 2019
 Researchers In Iceland Can Turn CO2 Into Rock. Could It Solve The Climate Crisis?, by Robin Young and Karyn Miller-Medzon, 10 December 2019