ATLANTA — Around 3 p.m. Monday, Tania Thompson pulled her car into the parking lot of the C.T. Martin Natatorium and Recreation Center for the second time in a day.

She and her neighbor had first come to cast their ballots shortly after the early-voting location had opened, but they found a line nearly wrapped around the building. They opted to return in the afternoon, hoping for a shorter line and warmer temperatures.

“I want to feel like my voice has been heard,” Thompson, 47, an immigrant originally from Jamaica, told The Washington Post. She said it was especially important at a time when her state is in the national spotlight and its voting system is under attack by President Trump.

“It’s nonsense,” she said of the president’s voting fraud claims. “I don’t feel like there is any merit to what he has been saying. All he’s doing is causing division. I just feel like he’s grasping at straws.”

Georgia voters streamed to early-voting locations Monday, the first day they could cast ballots in the extraordinary pair of runoffs that will culminate Jan. 5 and determine which party controls the Senate.

Voters cast ballots despite — and in some cases because of — the fusillade of baseless claims Trump has directed at Georgia officials in the weeks since he lost the state to President-elect Joe Biden in the Nov. 3 general election. For the first time since Trump began to wage his failed effort to overturn the results here and in several other swing states, voting commenced once again — with many casting ballots using the same Dominion machines the president’s allies have falsely claimed were rigged to benefit Biden.

The Georgia runoff pits Republican Sens. David Perdue and Kelly Loeffler against Democrats Jon Ossoff and the Rev. Raphael Warnock, pastor of Ebenezer Baptist Church. If both Democrats win, the party would knot the upper chamber at 50-50, with Vice President-elect Kamala D. Harris holding the tie-breaking vote after she is inaugurated.

Even as voters are being asked to resolve the Senate races — and as the electoral college formally cemented Biden’s win — sparring continued over the last round of voting.

An hour before Thompson pulled into the early-voting center’s parking lot, Georgia Secretary of State Brad Raffensperger held a news conference announcing an absentee ballot signature-match audit in Cobb County, an effort to once again demonstrate that the November election had been run properly and there was no evidence of widespread fraud.

“Now that the signature matching has been attacked again and again with no evidence, I feel we need to take steps to restore confidence in our elections,” Raffensperger said.

The Georgia Bureau of Investigation is assisting with the audit, which is expected to be completed before the Jan. 5 runoff.

Cobb County Elections Director Janine Eveler said her office will assist as required with the secretary of state’s order.

“I’m confident any audit would find our office followed procedures and only counted ballots that were processed correctly,” Eveler said in a statement. “Even though our resources are already stretched thin by advance voting and preparations for the January 5 runoff, we will help this process move as expeditiously as possible.”

Although there were no reports of significant problems on Georgia’s first day of early voting, the municipalities administering the election continue to be under the microscope.

The first day of voting continued apace, even though there were some reports of long lines and concerns about whether early-voting infrastructure was adequate.

“We are hopeful that the secretary of state has learned his lesson from early voting in the general election, in which he failed to provide the necessary eNet bandwidth to accommodate voters, a problem he did not fix until the third day,” said Seth Bringman, a spokesman for the Stacey Abrams-led Fair Fight Action. Bringman also said he hoped Raffensperger would lean on two counties to reopen “early-voting locations in areas where a disproportionate number of voters of color reside.”

Such pressure has already resulted in the reopening of early-voting locations in Cobb County, the third-most populous in the state.

This month, Cobb reduced its early-voting sites from 11 in the November general election to five for the Jan. 5 runoffs.

Critics, including the NAACP Legal Defense and Educational Fund, blasted the plan because three of the four shuttered sites were in the southern part of the county, which has the highest concentration of Black and Latino voters.

Johnny Gordon, a 65-year-old native of Atlanta, said he came to the community center to cast his ballot because amid all the controversy, he wanted to make sure his vote was locked in.

“I’ve heard all that, but it’s mostly noise,” he said. “As long as people are out here doing what they’re supposed to do, it’s going to be all right.”

Vanessa Williams in Washington contributed to this report.

CORRECTION: An earlier version of this report misspelled the name of the spokesman for Fair Fight Action as Seth Brinkman. It’s Seth Bringman.