During the coronavirus pandemic, a little-known German state lawmaker with an upbeat patter and a telegenic smile started railing on TikTok against pandemic regulations. Complaining about masks, vaccinations and other government requirements that he deemed "crazy," the lawmaker attracted millions of viewers with his videos by using an affable tone to deliver an anti-establishment message. Now, that lawmaker, Ulrich Siegmund, has harnessed his online popularity to come closer to power than any other far-right politician in Germany since the Nazi era ended in 1945.

Mr. Siegmund, 35, a former air freshener salesman, is the lead candidate for the Alternative for Germany party in Saxony-Anhalt, a state in eastern Germany where the party is projected to finish first in a statewide election on Sunday. If the party, known by its German initials, AfD, wins an outright majority, Mr. Siegmund will become the first far-right politician to govern a German state since the re-establishment of the country's democracy nearly eight decades ago.

That would be a convulsive moment for Germany's postwar political system, which was designed in the aftermath of World War II to prevent politicians deemed extremist from ever taking office. To the political establishment in Berlin, Mr. Siegmund's party is an outcast. The domestic intelligence agency has labeled it as "suspected extremist," an accusation it rejects as politically motivated.

Still, Mr. Siegmund has won over voters in Saxony-Anhalt, experts say, through his ability to present the party's hard-line policies in a more approachable and optimistic tone than many of his AfD colleagues, without distancing himself from extremists.