Mr. Mnuchin had made clear before the meeting that he wanted the governors to find someone who would push through the kind of cost-cutting and price increases that President Trump had publicly called for and that Treasury had recommended in a December 2018 report as a way to stem years of multibillion-dollar losses.

It was an unusual meeting at an unusual moment.

Since 1970, the Postal Service had been an independent agency, walled off from political influence. The postmaster general is not appointed by the president and is not a cabinet member. Instead, the postal chief is picked by a board of governors, with seats reserved for members of both parties, who are nominated by the president and confirmed by the Senate for seven-year terms.

Now, not only was the Trump administration, through Mr. Mnuchin, involving itself in the process for selecting the next postmaster general, but the two Democratic governors who were then serving on the board were not invited to the Treasury meeting. Since the meeting did not include a quorum of board members, it was not subject to sunshine laws that apply to official board meetings and there is no formal Postal Service record or minutes of what was discussed.

Nearly six months later, that meeting, along with other interactions between Mr. Mnuchin and the postal board, has taken on heightened significance as the Trump administration confronts allegations it sought to politicize the Postal Service and hinder its ability to handle a surge in mail-in ballots in November’s election. In interviews, documents and congressional testimony, Mr. Mnuchin emerges as a key player in selecting the board members who hired the Trump megadonor now leading the Postal Service and in pushing the agenda that he has pursued.

Mr. Trump’s animus toward the agency dates to at least 2013, but his criticism of its finances escalated once he took office and found new focus in late 2017, when he first bashed it for essentially subsidizing Amazon, another target of his ire. Amazon’s founder and chief executive, Jeff Bezos, owns The Washington Post, whose coverage has often angered Mr. Trump.

“This Post Office scam must stop. Amazon must pay real costs (and taxes) now!” the president wrote on Twitter on March 31, 2018, one of several such attacks over the years.

Twelve days later, he issued an executive order putting Mr. Mnuchin in charge of a postal reform task force. But it was not until earlier this year that the administration found a way to enforce its postal agenda — one that has now collided with the pandemic and the approaching election.

A few weeks after the February meeting with Mr. Mnuchin, one of the attendees, Robert M. Duncan, the chairman of the board of governors, who was appointed by Mr. Trump in 2017, threw a new name for postmaster general into the mix: Louis DeJoy.

Mr. DeJoy, a longtime logistics executive, was known for his hard-charging leadership style and his ability to convert disorganization into efficiency, as well his generous donations to the Republican Party, including to Mr. Trump. In October 2017, Mr. DeJoy had hosted a fund-raiser for the president’s re-election campaign at his North Carolina home.

His résumé was far different than recent postmasters general, most of whom had risen through the Postal Service ranks. Megan J. Brennan, who had announced in October 2019 her intention to retire as postmaster general at the end of January, began her career as a letter carrier in Pennsylvania.

Mr. DeJoy, who ran New Breed Logistics before selling it to XPO Logistics in 2014, would be coming from the private sector to assume control of a highly unionized, sprawling bureaucracy with more than half a million employees. His companies had experience working with the Postal Service, moving bulk shipments of packages from fulfillment centers and ferrying them to local Postal Service centers. But both companies had fewer than 10,000 employees, none of them unionized, and he had never worked in the public sector.

The companies were also the subject of a litany of complaints from workers, including more than a dozen lawsuits accusing managers — but not Mr. DeJoy personally — of presiding over a hostile environment rife with sexual harassment and racial discrimination and where workers were fired for getting sick or injured.

The board’s vice chairman at the time, David C. Williams, raised concerns about Mr. DeJoy’s candidacy and Mr. Mnuchin’s involvement, telling lawmakers during sworn testimony this week that he “didn’t strike me as a serious candidate.” Mr. Williams, a Democratic appointee, resigned before the vote as it became clear that Mr. DeJoy would be the pick.

Three months after the meeting in Mr. Mnuchin’s office, the board of governors announced Mr. DeJoy’s selection as the nation’s 75th postmaster general. Within weeks, he began carrying out changes, including cuts to overtime and limiting mail delivery trips. He curtailed postal hours and mandated that carriers must adhere to a rigid schedule. A July memo from the Postal Service warned that the changes might temporarily result in “mail left behind or mail on the workroom floor or docks.”

The measures matched up with recommendations in the task force report, which blamed the Postal Service for losing billions because of waste, inefficiency and a failure to respond to declining mail volumes.

But the rapid-fire moves just months before the November election concerned Postal Service insiders, who said that, since at least the Obama administration, the agency had generally sought to avoid significant changes within two or three months of a general election.

Soon, mail was piling up at post offices, veterans were not receiving their medications, bills were arriving late and questions began surfacing about the ability of the Postal Service to handle what is expected to be a record number of mail-in ballots this November because of the pandemic.

Amid an outcry from lawmakers, civil rights groups and state officials, Mr. DeJoy suspended many of the changes on Tuesday, including some that had been underway before he took the helm of the Postal Service. Yet he made clear during a Senate hearing on Friday that he planned to move ahead with “dramatic” measures after the election, including raising prices and limiting overtime.

Postal Service employees and union officials say significant damage has already been done. Hundreds of mail-sorting machines have been removed, and the day-to-day changes have caused confusion and delays among drivers, carriers and other workers.

In his Senate testimony on Friday, Mr. DeJoy chalked that up to growing pains as the organization tries to get leaner. “We all feel, you know, bad” he told lawmakers upset about mail delays affecting their constituents..

Over the last two years, Mr. Mnuchin met privately on multiple occasions about postal matters with Mr. Duncan, a former chairman of the Republican National Committee who was confirmed by the Senate as a postal board member in August 2018, according to people familiar with the meetings.

Mr. Mnuchin also arranged a meeting with John M. Barger, a California lawyer and financial investment adviser who was recommended to the Treasury secretary by a mutual associate who knew of Mr. Barger’s work as chairman of the board of the Los Angeles County pension fund. After a meeting in Washington, Mr. Mnuchin recommended that Mr. Trump appoint Mr. Barger to the board of governors.

Mr. Barger was confirmed by the Senate last summer, and was tapped to lead the committee to select a new postmaster general. He attended the February meeting in Mr. Mnuchin’s office with Mr. Duncan.

S. David Fineman, a former member and chairman of the Postal Service’s board, called Mr. Mnuchin’s close involvement in the affairs of the Postal Service “absolutely unprecedented.”