- The first interpretation of the question is that the writer wants to know whether Akkadian was the earliest (spoken) language. In that case the answer is no.
- Akkadian was written in cuneiform, so the writer could have been asking if cuneiform was the earliest script, in which case the answer is: "quite possibly."
Writing itself can be thought of as a language and the script can be thought of as a "rendering" of a spoken language, so for simplicity, I'm distinguishing the written representation of speech as a script (or writing); only the spoken language will be treated, as it is conventionally, as "language". For those who want a thorough explanation of the distinctions between spoken and written language, please read Barry B. Powell's Writing (2009).
Assuming the writer wants to know if the script used by speakers of the Akkadian language was the earliest script, the verdict is yet out. Egypt, China, and India can all make a similar claim -- that their script is oldest. Traditionally, the writing of Mesopotamia (including speakers of Akkadian) has been treated as the earliest. Dates for the oldest writing range from about 3500 B.C. to the end of the fourth millennium B.C., with cuneiform coming in at about 3400 (Powell).
Incidentally, for Mesomerica, another area that appears to have created (lexigraphic) writing on its own, the earliest found to date, comes from about 900 B.C., so it's not remotely in the running for earliest writing system.
The difference between language and script is sometimes clear and sometimes murky. The Greek language employs the Greek alphabet. The Hebrew "alphabet" is used for Hebrew. The Roman alphabet is used for the language of the Romans and the Romance languages, but it's also used for other languages, including English. Japanese uses systems of writing borrowed from the Chinese (Hiragana and Katakana), and another borrowed from the Romans (Romaji). Romaji is an alphabetic script, but Hiragana and Katakana are syllabaries, which means each symbol represents a syllable.
Akkadian used the same cuneiform system of writing as other groups centered around Mesopotamia.
The earliest of this (cuneiform) type of writing comes -- not from Akkadian speakers, but from Uruk (southern Iraq). In the late 4th millennium B.C., Sumerians made pictographic or iconic proto-Cuneiform writing with a pointed tool. The purpose of these documents was to record numbers of items for use in economic transactions. A representation of a sheep (a circle with a cross in the middle), for instance, with a numerical figure beside it could tell the number of sheep. The surface used could be wet clay, which hardened quickly, but could be reused. It could also be papyrus, but papyrus decayed in the climate. There was also a transition from tokens to bullae marked with cylinder seals to flat tablets, but that's a tangent not especially relevant here, except that the flat surface lent itself better than a curved one to cuneiform.
Gradually, the writing simplified, and curves in the drawings straightened out. This developed into writing, especially of the kind characterized as wedge-shaped or cuneiform because it was created using a triangular stylus that made the heads of the characters deeper than the tails, which trailed off. Head and trailing tail formed a wedge or nail shape. Developments in the proto-Cuneiform period included the clay writing surface, the stylus, lines in the clay to divide it into columns and cells, symbols, and, of course, content.
By 2700 B.C. the proto-cuneiform had evolved and cuneiform writing was used to communicate. There were royal inscriptions from that time written at Babylonia. Cuneiform letters have been found from 2400 B.C.
The Sumerians at Uruk developed the script, but the writing was taken over by speakers of other languages, notably Akkadian (the language used by the followers of Sargon [c. 2340 B.C.] who lived in a city of Sumer), and also Eblaite, Elamite, Hittite, Luwian, Hattic, Hurrian, and Urartian. These are diverse languages from different language families.
- "Archaic Uruk Cuneiform," by M. W. Green. American Journal of Archaeology, Vol. 90, No. 4 (Oct., 1986), pp. 464-466.
- "The Archaic Texts from Uruk," by Hans J. Nissen. World Archaeology, Vol. 17, No. 3, Early Writing Systems (Feb., 1986), pp. 317-334.
- Oriental Institute's Map of Mesopotamia shows Uruk, Sumer, and Akkad