A proprietary name for a form of artificial grass turf used chiefly as a playing surface in sports stadiums, Astroturf is from:
– Astro- in Astrodome, from the first use of Astroturf in the Astrodome stadium at Houston, Texas;
– the noun turf, denoting grass and the surface layer of earth held together by its roots.

The earliest occurrences of Astroturf that I have found are from an Associated-Press story published in several newspapers on Sunday 13^th March 1966—for example in the Fort Worth Star-Telegram (Fort Worth, Texas)—who ‘Smith’ is is not explained:

Houston (AP)—The Houston Astrodome will have an artificial infield covering for at least the start of the 1966 baseball season.
The man-made field, called Astroturf will be used on the infield and foul territories for the Astros’ pre-season games with the world champion Los Angeles Dodgers March 19-20.
“If the Astroturf works out as well as we anticipate we plan to cover the entire outfield with the material by mid-season,” club President Roy Hofheinz said Saturday.
Hofheinz said in the meantime play would be on an outfield sodded with Bermuda grass.
Smith said Astroturf has been developed as an engineered surface for athletic and recreational use.
Grass in the Astrodome died last year because of lack of sunlight when the glass sections of the dome were painted so players would not lose fly balls in the glare.
The new infield surface is portable and can be removed and put back within a few hours.

Incidentally, the following from The Pensacola News Journal (Pensacola, Florida) of Sunday 16^th February 1969 prefigures the metaphorical uses of Astroturf as opposed to grassroots:

There is a nationwide rebellion raging in our land and it all started at the grassroots level. The commotion has to do with the new look in recreational surfaces: synthetic grass.
Ever since Monsanto introduced “AstroTurf” back in the early 1960s in the famed dome stadium in Houston, the “Great Grass Rebellion” has been on.

With humorous allusion to grassroots—denoting the basic level of society or of an organisation—Astroturf metaphorically denotes simulated or artificially created public support for a policy, a movement, a product, etc., generated by an organised campaign. This sense arose from the idea that such a campaign is an artificial version of a grassroots campaign.

These are, in chronological order, the earliest occurrences that I have found of this metaphorical use—I have included the early occurrences of Astroturf humorously used in contrast to grassroots:

1-: From Instant populism (dated Saturday 3^rd June 1972 in Sam Smith’s Essays), by the U.S. author, political activist and social critic Sam Smith (born 1937):

Now everyone who’s anyone is a populist.
We have McGovern the populist. Humphrey taking populist stances. Muskie leaning towards populism. Jackson the conservative populist. Even Gore Vidal has joined the movement; he has been nominated to be secretary of state by the populist-leavened People’s Party of Dr. Spock, the well-known pediatric populist. If it keeps up, there is every possibility that Richard Nixon himself will campaign on a slogan of “Populism With Responsibility Under Law.”
I’m not complaining. It’s one of the healthier political trends in some time. […]
The problem is, however, that the people are being presented with a hastily prepackaged movement in the hope that they won’t come up with one of their own. A gaggle of conventional liberals are attempting to pass themselves off as authentic spokesmen spewed out of the alienation of the masses. It’s phony, of course. Hubert Humphrey is the same man he was before he (or his campaign managers) read Newfield & Greenfield’s the Populist Manifesto. McGovern is a run-of-the-mill liberal who shines only in comparison with his competition. Muskie is no more a creature of the people than Larry O’Brien. A media team can no more turn a candidate into a populist than an atom bomb can create Albert Einstein. The new populism, as filtered through the surviving Democratic candidates, rather than being a grassroots movement, is just a bunch of salesmen hawking Astroturf.

2-: From Students, Legislators Meet At Grass Roots, published in the St. Louis Post-Dispatch (St. Louis, Missouri) of Friday 1^st September 1972:

Student concern mixed with a little politics and some fun as the student Senate of Florissant Valley Community College experimented with meeting their public officials on a grass-roots level recently.
Later, the grass roots turned to Astro Turf, when both student [sic] and officials were guests of the baseball Cardinals at their game with the San Francisco Giants.

3-: From Grass roots or astro turf, published in The Gordon Journal (Gordon, Nebraska) of Wednesday 27^th October 1976—after giving an account of the city council’s vote rejecting the request for free ambulance service, the anonymous author writes:

This information was part of the city council proceedings carried on page 12 of last week’s Journal. For the way the vote went, refer to that paper and that page.
City council proceedings are carried each month in the Journal in the issue following the regular meeting of that board on the second Thursday of the month. There interested citizens will find, not only how their tax money was spent but all other business of the city complete with identification of councilmen proposing motions, who seconded same and just how each councilman voted.
For this service, the Journal receives three-fourths of the legal line rate, as established by law.
It would be interesting to conduct a poll to ascertain just how many people DO read council proceedings and proceedings of the county commissioners. While school board proceedings are not provided, the monthly bills do appear. The reason for publishing this informative material is to avoid the taint of secrecy—that the people may know, that is if they are at all concerned. Anyone who has any questions about the expenditure of money or any action or procedure of any of these boards is privileged to ask and to receive satisfactory answers.
Unless grass-roots government is as phony as astro-turf, this is the way it has to be.

4-: From Quarterbacking The Country, by Richard Reeves, published in the Richmond Times-Dispatch (Richmond, Virginia) of Wednesday 29^th October 1980:

San Antonio, Tex.—The crowd had been waiting almost an hour for Ronald Reagan and they burst into applause and cheers when he arrived. After all, he walked in with Roger Staubach.
Staubach, the former quarterback for the Dallas Cowboys, made his first political trip with the Republican candidate for president during this campaign. It may not be his last. A lot of people in Texas think that Staubach, now a sports commentator for CBS, will be a candidate for the U.S. Senate in 1982.
Roger the Dodger sort of denies that. “The reason I’m here is that I am a voter,” he told a crowd later in Corpus Christi. “I’m not a Republican. I’m not a Democrat. I’m a concerned citizen. I am a grass roots guy.”
Really he’s an Astro turf guy. Staubach is the most famous guy in Texas, an authentic hero after years of football bravery for the Cowboys and, before that, for the U.S. Naval Academy.

5-: From Tax-Overhaul Battle Follows Lawmakers Home, by Dale Russakoff and Anne Swardson, published in The Washington Post (Washington, D.C.) of Wednesday 7^th August 1985:

It remains to be seen whether Congress will trust the grass-roots pleas, or view them simply as orchestrated, down-home versions of Washington lobbying.
The insurance lobby learned this the hard way, after spending more than $5 million and generating 1.6 million pieces of mail to lawmakers opposing proposals to tax employe fringe benefits and the increased value of life insurance policies—known as “inside buildup.” Many tax-writers called the campaign overkill.
“A fellow from Texas can tell the difference between grass roots and Astro Turf,” Sen. Lloyd Bentsen (D-Tex.) said of his mountain of cards and letters from opponents of the insurance provisions. “This is generated mail.”

6-: From S.D. [= San Diego] City, County Battle on Growth Turns Bitter: Massive Spending by Builders Tilts Odds Facing Citizens’ Initiative on Limits, by Leonard Bernstein, published in the Los Angeles Times (Los Angeles, California) of Monday 31^st October 1988:

While their strength unquestionably lies in their campaign war chest, builders are touting a “grass-roots” campaign effort that includes 3,700 workers, an unknown number of them paid temporaries hired to walk precincts.
[…]
But the builders’ opponents dismiss the claims contemptuously. “That’s not grass-roots, it’s Astroturf,” snorted Peter Navarro, economic adviser for Citizens for Limited Growth, who said that the builders’ effort is based primarily around their ability to conduct frequent polls and spread “lies.”