Pete Buttigieg, who rose from obscurity to narrowly win the Iowa caucuses before dropping out of the Democratic presidential primary last month, has taken some of the first steps toward outlining his post-campaign future.

Mr. Buttigieg, the former mayor of South Bend, Ind., is forming both a political action committee, called Win the Era, and an affiliated nonprofit group, according to people briefed on the plans.

Donors have been told that the PAC will support and endorse candidates who represent generational change, specifically in down-ballot races, in hopes of helping to create a “pipeline” for the party. The groups will also promote issues such as climate change and cybersecurity.

A skeletal version of a website that refashions Mr. Buttigieg’s 2020 logo, replacing the word “Pete” with “Win the Era,” is already online, though it has not been advertised. “There is simply too much at stake to retreat to the sidelines now,” the site reads. “Together we can build the era that must come next.”