Mexicans will vote on Sunday in an election that is groundbreaking on several fronts: it’s set to be the largest race in the country’s history, it’s already among the most violent in recent memory, and it will likely put a woman in the presidency for the first time ever.

The two main contenders, who have largely split the electorate between them according to polls, are women. The front-runner is Claudia Sheinbaum, a climate scientist representing the ruling party and its party allies. Her closest competitor is Xóchitl Gálvez, a businesswoman on a ticket that includes a collection of opposition parties.

Ms. Sheinbaum has had a double-digit lead in the polls for months, but the opposition has argued those numbers underestimate the true support for their candidate. In an interview, Ms. Gálvez said “there is an anti-system vote,” and if Mexicans turned out in force on Sunday, “we will win.”

“She’s in the mind-set where she’s ahead by 30 points,” said Ms. Gálvez, of her rival. “But she’s going to have the surprise of her life.”

The contest showcases the immense strides in Mexico’s politics made in recent years by women, who weren’t even allowed to vote in the country until 1953. Both the top candidates come with considerable experience; Ms. Gálvez was a senator and Ms. Sheinbaum governed the capital, one of the largest cities in the hemisphere.

“For the first time in 200 years of the republic, we women will arrive at the highest distinction our people can give us: the presidency of Mexico,” Ms. Sheinbaum said in a recent speech.

Yet much of race has focused on a figure who isn’t on the ballot, but looms large: the powerful current president, Andrés Manuel López Obrador.

Mr. López Obrador has been a fixture of Mexican politics for decades, running for president in all three of the previous elections before finally winning in a landslide in 2018.

While broadly popular, Mr. López Obrador has been a polarizing figure, eliciting adulation from die-hard fans and vitriol from critics. His administration doubled the minimum wage and used cash transfer programs to help bring millions out of poverty, while empowering the military and pursuing measures that many warned would weaken democratic institutions.

His dominance upended establishment politics, prompting three parties, from the right, center and left, to form an uneasy union that is now backing Ms. Gálvez.

Ms. Sheinbaum has appealed to voters mainly by promising to continue his legacy. Ms. Gálvez has cast herself as an alternative for those unhappy with Mr. López Obrador’s leadership, vowing to reverse many of his policies.

“The way this election has played out is a testament to the impact López Obrador has had on Mexican politics,” said Carlos Bravo Regidor, a Mexican political analyst. “He is the center around which political identities and political positions are defined.”

Whoever succeeds Mr. López Obrador will face daunting challenges.

Cartel violence continues to torment the country, displacing people en masse and fueling one of the deadliest campaign cycles in recent Mexican history. Mr. López Obrador directed government attention to addressing the drivers of violence instead of waging war on the criminal groups, a strategy he called “hugs not bullets.”

Ms. Gálvez has slammed the approach.

“Enough of hugs for the criminals, and bullets for citizens,” she quipped on the campaign trail. She has said she would pull the armed forces out of civilian activities and direct them to focus on combating organized crime, while strengthening the police.

Ms. Sheinbaum has said she would continue to focus on the social causes of violence, but will also work to lower rates of impunity and build up the national guard.

On the economy, the opportunities are clear: Mexico is now the largest trading partner of the United States, benefiting from recent shift in manufacturing away from China. The currency is so strong it’s been labeled the “super peso.”

But there are also problems simmering. The federal deficit ballooned to around 6 percent this year, and Pemex, the national oil company, is operating under a mountain of debt, straining public finances.

“The fiscal risk we’re facing at the moment is something we haven’t seen for decades,” said Mariana Campos, director of México Evalúa, a public policy research group.

Another challenge involves the broad new responsibilities granted to the armed forces, which have been tasked with running ports and airports, running an airline, and building a railroad through the Mayan jungle. Ms. Sheinbaum has said “there is no militarization” of the country, while suggesting she’s open to re-evaluating the military’s involvement in public enterprises.

In addition to such pressing domestic challenges, the next president’s destiny will be intertwined with the outcome of the presidential election in the United States. A re-election victory for President Biden would provide continuity, but a return of Donald J. Trump to the White House would likely be far less predictable.

Mr. Trump’s plans to round up undocumented people on a vast scale and deport them to their home countries could target millions of Mexicans living in the United States. He has already threatened to slap 100 percent tariffs on Chinese cars made in Mexico.

Then there is the festering issue of fentanyl, which, the U.S. government says, cartels produce in Mexico using chemicals imported from China. Mr. Trump has suggested taking military action to combat the fentanyl trade.

Handling such pressure from Washington, even in the form of incendiary campaign rhetoric, could prove challenging to Mexico’s next president.

Ms. Sheinbaum has said Mexico would have “good relations” with either Mr. Trump or Mr. Biden as president, and her campaign team has said it will continue to work to contain flows of migrants.

Ms. Gálvez said she too, would be comfortable working with both men.

When asked how she would handle Mr. Trump, she said: “I’m accustomed to dealing with toxic masculinity.”

“It seems to me that Trump, at his core, is a pragmatic man,” she said, adding: “what he wants is to resolve the issues at the border and with fentanyl, and I think we can.”

Emiliano Rodríguez Mega contributed reporting from Mexico City.