The two-day Republican gathering in Atlanta was supposed to be something of a Trump-free zone.

The host, the conservative commentator Erick Erickson, did not include former President Donald J. Trump in the confab, and instead conducted 45-minute “fireside chat” interviews with six of his rivals for the Republican nomination. He told the crowd on Friday that Mr. Trump, and the criminal indictment handed down against him on Monday just 10 miles away, would not be a topic of discussion.

“We’ve got six presidential candidates — two governors, two senators, two members of Congress,” said Mr. Erickson, who is based in Georgia. “I want to ask them about policy questions.”

But even as the featured politicians tried to make their own cases without mentioning the former president, also the party’s current front-runner for 2024, his influence — and stranglehold over the Republican primary race — was palpable.

Former Vice President Mike Pence sidestepped a question about how he would close the polling gap with Mr. Trump. Nikki Haley, the former governor of South Carolina who served as United Nations ambassador under Mr. Trump, thinly complimented the former president even as she explained why she was running against her former boss. Gov. Ron DeSantis of Florida, Mr. Trump’s closest rival, said he hoped that the party would focus more on the future than “some of the other static that is out there.”

On and offstage, participants and attendees alike said they believed that defeating President Biden would not be possible as long as the party repeated Mr. Trump’s assertions that the 2020 election was stolen.

Georgia will play a pivotal role in the outcome of the general election, both because of recent election outcomes and because the state has the jurisdiction in the most recent Trump indictment. It’s why current and former state officials have been vocal about their belief that having Mr. Trump at the top of the ticket risks delivering a message that is more focused on 2020 election denialism than policy — one that could hurt their chances of winning in the key battleground state.

“It should be such an easy path for us to win the White House back,” said Gov. Brian Kemp, one of the few figures who was asked about and who directly addressed Mr. Trump. “We have to be focused on the future, not something that happened three years ago.”

Mr. Trump is expected to skip the first Republican debate next week and post an interview with the former Fox News host Tucker Carlson that night instead. He still has a solid, double-digit lead over his rivals, according to recent state and national polls.

At the weekend event, themed “Forward: Which Way,” attendees saw a chance to hear voices other than Mr. Trump’s. Senator Tim Scott of South Carolina, who is in single digits in most national polls, vowed to give governors more power in federal decisions and stayed true to his positive, faith-based message. Mr. DeSantis gave highlights from his family’s recent campaign trip to the Iowa State Fair while emphasizing the policies he has passed in Florida. Vivek Ramaswamy, the entrepreneur and author who has received attention recently from voters and rivals alike, spoke of a “revolution” in changing how the federal government operates.

Former Gov. Chris Christie of New Jersey, Mr. Trump’s most vocal critic, largely avoided mention of the former president but later railed against him to reporters outside the event, calling him “a coward” for not joining the debate on Wednesday, adding, “He’s afraid of me, and he’s afraid of defending his record.”

While many in the crowd expressed frustration over Mr. Trump’s legal troubles, they also said that Monday’s indictment was little more than a politically motivated sideshow that distracted from larger policy issues.

Electing a candidate who can defeat Mr. Biden in the general election remained their chief objective — one that many attendees said would be challenging if Mr. Trump’s campaign message focused more on his 2020 grievances instead of policy.

“Honestly, we need a new generation,” said Lyn Murphy, a Republican activist who attended Friday’s gathering. “We’ve got a great bench.”

Bill Coons, 58, who identified himself as a political independent who voted for a third-party candidate in 2016 and supported Mr. Trump in 2020, said he probably would not support Mr. Trump if he became the party’s nominee.

“Why talk about the past when you’ve got a future to move towards?” he said. “The future of this nation is dire if Biden is re-elected, in my opinion.”

Although Georgia has long been a Republican stronghold, voters there chose Mr. Biden in 2020, making him the first Democrat in nearly 30 years to win the state. It also sent Democrats to the U.S. Senate in two 2021 runoff races, and re-elected Senator Raphael Warnock, a Democrat, in 2022 for a full term.

When asked about her role in the Trump administration, Ms. Haley called Mr. Trump “the right president at the right time.”

But “at the end of the day, we have to win in November,” she said. “And it is time to put that negativity and that drama behind us.”