As the global economy heats up and tries to put the pandemic aside, a battle for the young and able has begun. With fast-track visas and promises of permanent residency, many of the wealthy nations driving the recovery are sending a message to skilled immigrants all over the world: Help wanted. Now.

In Germany, where officials recently warned that the country needs 400,000 new immigrants a year to fill jobs in fields ranging from academia to air-conditioning, a new Immigration Act offers accelerated work visas and six months to visit and find a job.

Canada plans to give residency to 1.2 million new immigrants by 2023. Israel recently finalized a deal to bring health care workers from Nepal. And in Australia, where mines, hospitals and pubs are all short-handed after nearly two years with a closed border, the government intends to roughly double the number of immigrants it allows into the country over the next year.

The global drive to attract foreigners with skills, especially those that fall somewhere between physical labor and a physics Ph.D., aims to smooth out a bumpy emergence from the pandemic.

Covid’s disruptions have pushed many people to retireresign or just not return to work. But its effects run deeper. By keeping so many people in place, the pandemic has made humanity’s demographic imbalance more obvious — rapidly aging rich nations produce too few new workers, while countries with a surplus of young people often lack work for all.

New approaches to that mismatch could influence the worldwide debate over immigration. European governments remain divided on how to handle new waves of asylum seekers. In the United States, immigration policy remains mostly stuck in place, with a focus on the Mexican border, where migrant detentions have reached a record high. Still, many developed nations are building more generous, efficient and sophisticated programs to bring in foreigners and help them become a permanent part of their societies.

“Covid is an accelerator of change,” said Jean-Christophe Dumont, the head of international migration research for the Organization for Economic Cooperation and Development, or O.E.C.D. “Countries have had to realize the importance of migration and immigrants.”

The pandemic has led to several major changes in global mobility. It slowed down labor migration. It created more competition for “digital nomads” as more than 30 nations, including Barbados, Croatia and the United Arab Emirates, created programs to attract mobile technology workers. And it led to a general easing of the rules on work for foreigners who had already moved.