Im not sure Cyrillic WAS invented, so much as grew.
Look at mediæval texts - Cyrillic and Greek are almost the same. I think they just started writing Slavic languages in Greek, dissimilating beta from veta, throwing in Shin from Hebrew for the 'sh' sound, and running from there.
Once you've done that, you need hard and soft signs, then combine a i with a and o to get Ya and Yu, and youre pretty much there....