Mayor Karen Bass had a choice to make.

She had been in a senior staff meeting, preparing for a news conference with California’s governor, Gavin Newsom. They were planning to trumpet the progress of the recovery from the January wildfires that destroyed thousands of her constituents’ homes.

But then she started getting messages that heavily armed agents and soldiers were descending on MacArthur Park, a hub in one of the densest immigrant neighborhoods in Los Angeles. She had been regularly texting with a top federal official leading the immigration raids to coordinate a meeting but said she had been given no warning on the show of force unfolding at the park on a Monday afternoon in July.

Ms. Bass told her staff to skip the governor’s event and take her instead to the park. She was soon confronting federal agents, demanding to speak to whoever was in charge.

“My comment is, they need to leave,” she told an agent, shouting over the thudding of helicopters overhead, visibly angry, as news crews jostled around her. “And they need to leave right now. Because this is unacceptable.”

Ms. Bass has since framed the last-minute decision to challenge the agents at MacArthur Park as a natural response to an unfolding crisis. But the image of her facing down a literal Trump administration army has proved pivotal for a leader who only months ago was confronting a well-funded recall campaign.