I was speaking slightly out-of-hand, but it's the natural conclusion if you take the writings to have been authentically authored by Moses.

Religious traditions place him in approximately the middle of the 2nd millenium BC, while secular scholarship, when they assume he even existed, put him in the 13th century BC. There are numerous scholarly sources attesting to the fact that Hebrew only began to exist as a language in about the 10th century BC. Ergo, Moses must have written in a pre-Hebrew language, which would have very likely been Ugaritic, or at least a related dialect.

This is backed up by the fact that there are certain portions of the Old Testament that are written in a form of Hebrew which is comparatively archaic, such as the Song of Moses in Deuteronomy and the middle chunk of the Book of Job. You can see this reflected in the 2nd century BC Greek translation, the Septuagint, wherein various chunks of these texts are skipped, apparently on account of the translators being unsure how to translate what would be comparable to Middle English to us.

The earliest parts were written in a early form of Hebrew which existed roughly at the same time as Ugaritic, a closely related language. However, this early Hebrew was not Ugaritic, which had sounds, words, and grammar that was quite distinct from any historical or pre-historical Hebrew.