Rockets were being made long before 50 years ago. There were plenty of rockets in WWI. And there were smaller rockets going back to before the US war of independence (ie "the rocket's red glare"). If we are talking big metal things that fly into space being produced on an assembly line, then those operating in Germany during late WWII making the V2s (75years ago) were probably the first rocket factories. But I'm not going to clap for them.

Technically, military rockets were not a thing that existed at the time of the US war for independence. The phrase "the rocket's red glare" refers to Congreve rockets, which were invented in the 19th century following the introduction of rockets into modern military use in India at the end of the 18th century.

https://en.wikipedia.org/wiki/Congreve_rocket

The Congreve rockets were inspired by the rockets used by Mysore starting in 1780. So there were military rockets in use at the time of the US war of independence, they just weren't being used by either of the combatants in that war.

"The Star-Spangled Banner" was written during the War of 1812, not the War of Independence.

Rockets with orbital capability are a whole different ballgame.

(The Mongols used rockets several hundred years ago, but back then no one even knew what an orbit was).