How do we know that other factors drove global warming just 10,000 years ago, but CO2 drove it in the late 1970s?

Scientists debate why mammoths went extinct - CTV News

CHERSKY, Russia — During the last Ice Age, shaggy mammoths, woolly rhinos and bison lumbered across northern Siberia. Then, about 10,000 years ago -- in the span of a geological heartbeat, or a few hundred years -- the last of them disappeared.
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No one knows for sure what set off global warming back then -- perhaps solar activity or a slight shift in the Earth's orbit.
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During the transition from the ice age to the modern climate, global temperatures rose 5 degrees Celsius, or 9 Fahrenheit. But in Siberia's northeast the temperature soared 7 degrees, or nearly 13F, in just three years, the elder Zimov said.
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Adrian Lister, of the paleontology department of London's Natural History Museum, said humans may have delivered the final blow, but rapid global warming was primarily responsible for the mammoth's extinction. It brought an abrupt change in vegetation that squeezed a dwindling number of mammoths into isolated pockets, where hunters could pick off the last herds, he said.

People "couldn't have done the whole job," he told AP Television News.