Pre-Islamic Arabia was home to a variety of languages, we know this from the inscriptions speakers of those languages left. For example, Dadanitic was spoken in Dadan, and Taymanitic in Tayma'; both in the north of modern-day Saudi Arabia. Saba’ic, Ma’inic (Minaic), Qatabanic, and Hadramawtic were spoken in South Arabia (Yemen).

As for Arabic, it certainly existed before the seventh-century as both a spoken and written language. The Arabic script, too, predates the seventh-century. Though it had continued to develop into the Islamic era. Arabic inscriptions written in the Arabic script date to the sixth-century, older Arabic inscriptions were written in a non-Arabic script, like the Namara inscription for example, which is dated to the fourth-century CE and was written in the Nabataean Aramaic script.

By the seventh-century, only two languages seem to have survived, Arabic and Saba'ic. The latter was already in decline by then, as its speakers, the Himyiarites, were subjugated by the Abasynians (Ethiopians) in the sixth-century, and subsequently by the Persians.

Sources

Robert Hoyland, Arabia and the Arabs

Greg Fisher (ed), Arabs and Empires before Islam