Shoebox-sized satellites being developed by SpaceX and other companies to help expand U.S internet access could get off the ground faster under a plan announced July 9 by Federal Communications Commission Chairman Ajit Pai.

The order, set for a vote at the FCC’s Aug. 1 meeting, would help Elon Musk’s Space Exploration Technologies Corp., Amazon.com Inc., Boeing Co., and other companies deploy thousands of the small satellites that can beam high-speed internet connections to unserved parts of the...