In the weeks after Joseph R. Biden Jr. was elected president, advisers delivered a warning: His approach to immigration could prove disastrous.

Mr. Biden had pledged to treat unauthorized immigrants more humanely than President Donald J. Trump, who generated widespread backlash by separating migrant children from their parents.

But Mr. Biden was now president-elect, and his positions threatened to drastically increase border crossings, experts advising his transition team warned in a Zoom briefing in the final weeks of 2020, according to people with direct knowledge of that briefing. That jump, they said, could provoke a political crisis.

“Chaos” was the word the advisers had used in a memo during the campaign.

They offered a range of options to avert that crisis, by better deterring migrants. Mr. Biden seemed to grasp the risk. But he and his top aides failed to act on those recommendations.

The warnings came true, and then some. After Mr. Biden became president, migrant encounters at the southern border quickly doubled, then kept rising. New arrivals overwhelmed border stations, then border towns, and eventually major cities like New York and Denver.

Anger over illegal migration helped return Mr. Trump to the presidency, and he has enacted even more aggressive policies than those Mr. Biden first campaigned against. Mr. Trump has drawn outrage from Democrats by sending masked agents to target immigrants, often aided by National Guard soldiers.

But a New York Times examination of Mr. Biden’s record found that he and his closest advisers repeatedly rebuffed recommendations that could have addressed the border crisis faster, and eased what became a potent issue for Mr. Trump as he sought to return to the White House and justify the aggressive tactics roiling American cities today.

Former Biden administration officials told The Times that Mr. Biden and his circle of close confidants — including Ron Klain, who was chief of staff during the president’s first two years, Mike Donilon, Jennifer O’Malley Dillon and Anita Dunn — made two crucial errors.

First, they underestimated the scale of migration that was coming. Second, they failed to appreciate the political reaction to that migration — believing that stronger enforcement would alienate Latino and progressive voters, and also that a border surge would not be an important issue to most voters. Those calculations would later prove to be mistaken, with many voters, including Latinos, citing immigration as a reason for supporting Mr. Trump in 2024.

“Everybody was reacting to the excesses of the Trump administration,” said Cecilia Muñoz, who helped shape immigration policy in the Obama administration and oversaw domestic and economic policy for the Biden transition team.

Yet as public concern over border security grew, partly in response to Mr. Biden’s own actions, his administration proved catastrophically slow to change course, former aides said. The president and his closest aides treated immigration as a distraction from other issues, such as the coronavirus pandemic and the economy.