“The U.S. is not the strong, solitary economic power that it was in the past. It was so overwhelming in its economic power that it could almost unilaterally determine what was going to happen,” said Tom Bernes, a fellow at the Centre for International Governance Innovation who was previously a Canadian representative at international financial institutions. “But the world is changing.”

Yet, the Trump administration may not pose the threat many initially feared. Compared with plans to reduce funding in federal government departments, the proposed budget cut is but a minor deviation from President Obama’s commitment. And more moderate advisers, like Gary D. Cohn, the director of the National Economic Council, and H. R. McMaster, the national security adviser, are trying to steer policy in an internationalist direction.

Both institutions have worked to ingratiate themselves with the administration.

The World Bank, for example, has pledged to advise the administration on infrastructure investment. And it has certainly not hurt that its head, Jim Yong Kim, has developed a close working relationship with Ms. Trump after meeting her a few months ago.

Last week, Mr. Trump proclaimed his support for Mr. Kim, whose legitimacy came into question after his presidency was extended hurriedly ahead of the November election.

The Women Entrepreneurs Finance Initiative unveiled at the Group of 20 meeting came out of Ms. Trump’s conversations with Prime Minister Justin Trudeau of Canada and then Mr. Kim. According to the World Bank, the idea was formally brought to the organization during a March meeting by a German official, who said the proposal came from the White House.

The facility was set up with a speed unusual at the World Bank and will use the $325 million raised through donors to draw commercial finance. Its goal is to help women in developing countries gain access to the funding, technical assistance and networks needed to start businesses.

The White House says Ms. Trump, who wrote her book “Women Who Work” before her father became president, will not be involved in operations and fund-raising. Ms. Trump, who briefly sat in for her father at sessions in Hamburg this month, serves as a senior adviser to the president. Beyond her official role, however, political analysts say it is Mr. Kim’s relationship with the first daughter that has proved pivotal given Mr. Trump’s emphasis on personal connections and keeping his family involved in his administration.