Elon Musk’s SpaceX aims to make history once again this week, highlighting the benefits of reusable boosters with the scheduled launch of the first large liquid-fueled rocket powered by engines previously fired in space.

Relying on the Falcon 9’s repurposed lower stage—including nine refurbished main engines intended to propel a European commercial satellite into Earth’s orbit—the blastoff slated for Thursday from Florida’s Kennedy Space Center will mark the culmination of years of intense planning, testing and public advocacy...