U.S. airlines would be able to hire new pilots with far less cockpit experience than currently required under a proposal aimed at addressing a staffing shortage, a move likely to rekindle a debate over aviation safety.

Certain military pilots with as little as 500 hours of flying experience would be allowed to become commercial co-pilots, according to people familiar with an advisory panel’s recommendations, compared with the mandatory at least 750 hours required today. That is already down sharply from the minimum of 1,500...