PHOENIX — This spring, Mark Finchem traveled to Mar-a-Lago for the premiere of a documentary advancing the specious notion that the 2020 presidential election had been stolen from President Donald J. Trump by an army of leftists stuffing drop boxes with absentee ballots. As a state representative and candidate for secretary of state in Arizona, Mr. Finchem was a minnow among the assembled MAGA stars, the likes of Rudolph W. Giuliani and Representative Marjorie Taylor Greene of Georgia.But he still got his face time.“President Trump took 20 minutes with me,” Mr. Finchem later recounted during a campaign stop. “And he said: ‘I want you to understand something. The Arizona secretary of state race is the most important race in the United States.’”Arizona, of course, occupies a special place on Mr. Trump’s map of election indignities — as the onetime Republican stronghold where President Biden’s narrow and crucial victory was first called by, of all networks, Fox News. Should Mr. Trump run again in 2024, a friendly secretary of state, as administrator of the state’s elections, could be in a position to help him avoid a repeat.Now, as Arizona prepares for its primaries on Tuesday, Mr. Finchem is the candidate of a Trump-backed America First coalition of more than a dozen 2020 election deniers who have sought once-obscure secretary of state posts across the country. While most of them have been considered extremist long shots, a recent poll gave Mr. Finchem an edge in Arizona’s four-way Republican race, though a significant majority of voters are undecided.Mr. Finchem’s campaign pronouncements are testament to the evolution of the “Stop the Steal” movement: It is as much about influencing future elections as it is about what happened in 2020.Mark Finchem, a proponent of the “Stop the Steal” narrative, appeared with former President Donald J. Trump at a rally this past month in Prescott Valley, Ariz.Ash Ponders for The New York TimesTo that end, Mr. Finchem, who has identified himself as a member of the Oath Keepers militia in the past, may be the perfectly subversive candidate. Like his America First compatriots, he seeks, quite simply, to upend voting.He wants to ban early voting and sharply restrict mail-in ballots, even though the latter were widely popular in Arizona long before the pandemic. He is already suing to suspend the use of all electronic vote-counting machines in Arizona, in litigation bankrolled by the conspiracy theorist and pillow tycoon Mike Lindell. And he has co-sponsored a bill that would give the state’s Republican-led legislature authority to overturn election results.If he loses his own race, Mr. Finchem told a June fund-raiser, “ain’t gonna be no concession speech coming from this guy.”Mr. Finchem did not respond to requests for comment for this article, and one of his lawyers declined to comment. But in a May email he assured Republican supporters that if he had been in office in 2020, “we would have won. Plain and simple.” In the days after the election, he was co-host of an unofficial hearing at a downtown Phoenix hotel where Mr. Giuliani, Mr. Trump’s personal lawyer, aired bogus stolen-elections claims. He was instrumental in trying to advance a slate of fake Trump electors in Arizona — part of a scheme to overturn the elections in a number of states that is being investigated by the Justice Department — and he is helping gather signatures to petition to decertify the state’s election results, even though that is not legally possible.Key Revelations From the Jan. 6 HearingsCard 1 of 9Making a case against Trump. More