The cuneiform script is a phonetic writing system that records the syllable using very evolved and stylized pictures of common items (this is similar to the way hieroglyphic writing came about in Egypt).
Figuring it out involved a lucky find, obviously; Akkadian is an extinct language inside a living language family, and is extinct in the same way really old Old English is extinct; learning Old English wouldn’t be too difficult for modern native English speakers, and the translator of Akkadian made some guesses, tested them, found some sequences which looked like words which had been passed down, and laboriously reconstructed many of the sounds as well as the language itself.
IOW, it wasn’t easy.
As noted above, the non-Akkadian origin was clear from the sound assignments to many of the “pictures” — they didn’t correspond to the Akkadian language, but the writing system had been in use and was teachable, so the Akkadians were stuck with the Sumerian forms. Sumerian was used as a ceremonial language for centuries after the everyday spoken version (as well as the ethnic group) vanished from the Earth.
I always enjoy the articles you find.
Their language is now understood to have many Dravidian elements, although it was advanced well beyond all such languages at the time writing was invented ~ probably driven by writing itself. At the same time the Sa'ami languages are also quite arguably Sumerian cognates ~ but the problem is that it's only been within the last few hundred years any of them were rendered into writing, while at the same time they've been heavily influenced by Indo-European and Fenno-Ughric languages.
Archaeologists in Iran are working on an ancient pre-Sumerian settlement/city/town/whatever that appears to connect ancient Mesopotamia with ancient South India.
Most of the above was predicted shortly after the first translations were made of early Sumerian texts ~ and simply on the basis that the Sumerians discussed Ice Flows, Glaciers and sunny beaches with palm trees (at least the way the early Hungarian translators understood the texts).
The Great Depression and WWII/Communist occupation/etc. left careful examination of Sumerian materials in the lurch for a very long time. Scholars are just now getting back into the wealth of untranslated materials.
Thanks!