Prove originality of the Hebrew language in Bible

I heard that critics claim that there was no Hebrew language at the time of the exodus, not until the Davidic kingdom was established. Hence if that's true what language would Moses and the Israelites have spoken?

Those "critics" may have certain (unproved) theories, but the unbroken chain of Jewish tradition says that the first and original language of the world, until split into 70 languages in the Tower of Babel (Breishit 58), was Hebrew. This was always God's language from creation ("and God said (!) let there be light"), and how He gave the Torah and spoke to all of the prophets, and logically, why should the eternal God change?! Even Adam, the very first person, received his name because he was formed from the Adama (=earth, Breishit 2, 7; 5, 2), a derivative which is not logical in any other language but Hebrew. The Torah itself writes that Joseph already identified himself to Potiphar as a Hebrew (see Breishit 39), and he convinced his brothers that it's really him, by speaking Hebrew to them (ibid, 45, 12). The midrash (Vayikra Rabba 32) reveals that our forefathers in Egypt were careful not to assimilate nationally, by continuing to use the Hebrew language and Hebrew names. In fact, the 12 sons of Jacob went down to Egypt with classic Hebrew names (Reuven, Shimon, Levi… see the root and meaning of their Hebrew names in Breishit 29 & 30), and after 210 years, the tribes left Egypt with those same 12 Hebrew names (Bamidbar 1). The heads of those tribes who left Egypt, also had perfectly Hebrew names, e.g. Nachshon ben Aminadav, Eliav ben Cheilon, Netanel ben Tzu'ar etc., Bamidbar, ibid), which are understandable even to the modern Hebrew-speaking child! It's important to remember, that even if critics may claim that something hasn't been found, logic says that you can't prove anything from something that hasn't (yet!) been found. Especially when Israeli archeology is constantly digging and revealing deeper findings (most recently found in Jerusalem, the Judean King Hezekiah's personal seal from 2,700 years ago!, see https://www.biblicalarchaeology.org/daily/news/king-hezekiah-in-the-bible-royal-seal-of-hezekiah-comes-to-light/), verifying the truth of the Jewish and Bible traditions. With Love of Israel, Rav Ari Shvat (Chwat)