Experts believe the future of the First Amendment could be at stake, with the case expected to test the legal definition of political free speech in the United States.
The trial was delayed after Ms Palin tested positive to Covid-19 on 24 January - the day it was due to begin.
The unvaccinated former Alaska governor was spotted dining maskless at New York City restaurants both before and after being diagnosed with Covid, flouting regulations that customers must provide proof of vaccination before entering restaurants.
Ms Palin, 57, is suing the Times over an editorial that incorrectly connected linked the 2011 shooting of US congresswoman Gabby Giffords to a map circulated by her political action committee showing Democratic districts in crosshairs.
The article was published under deadline pressure on the day gunman James T Hodgkinson fired on a group of Republican lawmakers at a baseball practice in Alexandria, Virginia, in June 2017.
The Times quickly corrected the error but Ms Palin was not satisfied and launched a libel lawsuit in 2017 alleging it had acted with malice.
That lawuit was dismissed after a judge ruled Ms Palin’s lawsuit had failed to show the newspaper knew it was publishing false statements in an editorial before quickly correcting them.
In releasing his decision that the suit failed to show “actual malice”, US District Court Judge Jed Rakoff made the memorable remark: “Nowhere is political journalism so free, so robust, or perhaps so rowdy as in the United States. In the exercise of that freedom, mistakes will be made.”
However, Judge Rakoff’s decision was overturned by a federal appeals court, leaving the 2008 Republican nominee for vice president free to pursue the libel case.
Ms Palin is seeking unspecified damages, and according to court papers she has estimated damages of $421,000 to her reputation.
The case is expected to test the precedent-setting 1964 Supreme Court New York Times vs Sullivan ruling which found public officials must prove “actual malice” when a defamatory error is published.
The complaint alleges James Bennet, the former editor of the Times’ editorial board, had “actual knowledge that the false and defamatory statements he wrote and The Times published about Mrs Palin were untrue”.
“Alternatively, Mr Bennet and The Times published the Palin Article with reckless disregard for and a purposeful avoidance of the truth.”
Times spokesman Jordan Cohen told The Independent they were seeking to “reaffirm a foundational principle of American law: public figures should not be permitted to use libel suits to punish unintentional errors by news organisations.
“We published an editorial about an important topic that contained an inaccuracy. We set the record straight with a correction.
“We are deeply committed to fairness and accuracy in our journalism, and when we fall short, we correct our errors publicly, as we did in this case.”
Washington Post media columnist Erik Wemple wrote that the case would “demarcate the line between really bad journalism and libelous journalism”.
First Amendment attorney Ted Boutrous told CNN that Ms Palin “faces an enormously steep uphill battle” to win the libel case.
“This lawsuit has always seemed to me to be part of a disturbing trend in recent years of high-profile political figures misusing libel suits as political stunts intended to chill speech on matters of public concern — exactly what the First Amendment forbids,” he said.
The trial was due to begin jury selection on 24 January, however Judge Rakoff announced that day Ms Palin’s positive Covid result.
“She is of course unvaccinated,” the judge said.
It soon emerged that Ms Palin had been spotted maskless at Elio’s, an Italian fine dining restaurant on the city’s Upper East Side, on Saturday night.
The next day she was seen dining maskless at Campagnola in Manhattan, before returning to Elio’s again on Wednesday where she dined outside.
Elio’s restaurant’s manager apologised for allowing Ms Palin to dine without showing proof of and said it was taking the “unfortunate oversight very seriously”.
After she was nominated as John McCain’s running mate in 2008, Ms Palin became increasingly critical of her press coverage and coined the phrase “lamestream media” to describe what she felt was a liberal bias in presidential election campaign coverage.
In a viral interview with then-CBS anchor Katie Couric, Ms Palin couldn’t name a single media source she consumed, claiming she read “all of them, any of them that have been in front of me over all these years”.
Ms Palin was parodied by Tina Fey on Saturday Night Live, with the comedian poking fun at her foreign policy credentials with the line: “I can see Russia from my house”.
In a court filing on 17 January, the Times said Governor Palin was already seen “as a controversial figure with a complicated history and reputation, and in the time since the editorial was published, Gov. Palin has prospered”.
On her personal website, Ms Palin claims to offer “journalism reporting on current events” and touts her three “New York Times best-selling books” .
when historians write about the last hour they will begin by noting the 2008 republican vp nominee was rapping on tv dressed as a bear, then the network cut to trump announcing coronavirus flight suspensions, then tom hanks got it & the nba suspended https://t.co/QlJDDHMWtS— David Mack (@davidmackau) March 12, 2020
During preliminary arguments, Ms Palin sought to have footage of performance on The Masked Singer reality TV show withheld from the jury.
She appeared on the show on 11 March 2020 - the same day Tom Hanks tested positive for Covid-19 and the NBA announced it was suspending its season - dressed in a bright pink bear costume singing Baby Got Back by Sir Mix-a-Lot.
During arguments over jury selection, her lawyers sought to ask the prospective panelists whether they had any opinions about her, the Times, or the media.
Jury selection begins on Thursday, with opening arguments scheduled to begin next week. The trial is expected to last five days.
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