"Invented" is doing a lot of legwork here. Rockets have been invented in China in the 13th century, if not earlier. Hwacha ("fire cars") were more advanced than that, since they were an early version of an MLRS which could fire over a hundred rocket arrows at once. But Chinese Huoche (the same word with the same meaning) seems to predate Hwacha, introduced probably somewhere in the late 14th century[1].

Hwachas were probably more of a further development of the earlier Huoche than a completely new invention.

[1] https://en.wikipedia.org/wiki/Hwacha

Is the 15th century really "ancient"?