The debate between President Biden and former President Donald J. Trump this week will be the highest-stakes moment of their rematch, plunging two presidents into an extraordinarily early confrontation before a divided and angry nation.

For Mr. Biden, the debate in Atlanta offers an opportunity to remind voters of the chaos of his predecessor’s leadership, his criminal convictions and to warn of an even darker future should he win a second term. For Mr. Trump, it’s a chance to make his case that America has grown more expensive, weaker and more dangerous under his successor.

But the face-off on Thursday also poses significant risks for the two men — both of them the oldest candidates ever to compete in a presidential race — who have been locked in a contentious rivalry defined by mutual hatred for more than four years. That animosity heightens the evening’s unpredictability. A notable misstep — a physical stumble, a mental lapse or a barrage of too-personal insults — could reverberate for months, because of the unusually long period until they meet again for the second debate in September.

“This is a big inflection point,” said Karl Rove, a leading Republican strategist who guided George W. Bush’s two successful presidential runs. “Can Biden be consistently cogent, causing people to say, ‘Well, maybe the old guy is up to it?’ And is Trump going to be sufficiently restrained that people say, ‘You know what, it really is about us, not about him?’”

This presidential debate will be the earliest in the nation’s history and notably different from those familiar to many Americans. Hosted by CNN rather than a nonpartisan commission, it will be simulcast on more than five networks, without a live audience and without opening statements. Each candidate will have two minutes to answer questions, followed by one-minute rebuttals and responses to the rebuttals, and their microphones will be muted when it is not their turn to speak.

The two men are taking strikingly different approaches to their preparation. Mr. Biden hunkered down with his aides at Camp David for formal debate sessions, with the part of Mr. Trump expected to be played by Bob Bauer, the president’s personal attorney. The former president is taking a looser approach but is participating in more “policy sessions” than he held in 2020.