To answer the question, here is an excerpt from Deciphering the Proto-Sinaitic Script (pages 202 & 203):
[D]espite all the polemics surrounding the Exodus story, one element of proof remains that cannot so easily be discounted or ignored: The proto-Sinaitic scribal tradition did make its way from out-of-Egypt, and it did indeed reach the land of Canaan (presumably along with the scribes who made use of the script). For this reason, the importance of the proto-Sinaitic script cannot be overstated—it is really at the crux of the whole Exodus debate. There, once it made its way into Canaan and surrounding areas, proto-Sinaitic writing would continue to change until it eventually developed into various forms—into these descendant scripts that we know of today. Canaanite/Phoenician alphabetic writing forms the basis for the Hebrew, Arabic, Greek and Roman alphabets—ones that would in time, incredibly, spread over the surface of the globe. When taking this incredible human legacy into due consideration, it is extraordinarily remarkable to see how the origins of proto-Sinaitic writing, as the progenitor behind the whole alphabetic tradition, to say the least, are more than awkwardly intertwined with the biblical narrative. Ultimately, the proto-Sinaitic script remains central for those biblical scholars looking to understand the origins of the Sinai covenant. The Hebrew Bible certainly does not provide any explanation whatsoever of where the writing system employed by the Jewish patriarchs and matriarchs comes from. In fact, in the relevant passages where writing is mentioned in the Bible, it is just plainly taken for granted that it exists! For instance, in the Book of Exodus, when Moses receives the tablets from God on Mount Sinai, there is not one word to explain where the writing system being employed originates, for it is simply written, “When the LORD finished speaking to Moses on Mount Sinai, he gave him the two tablets of the covenant law, the tablets of stone inscribed by the finger of God” [Exo. 31: 18, NIV]. And much the same goes for another related passage: “The tablets were the work of God; the writing was the writing of God, engraved on the tablets” [Exo. 32: 16, NIV].
Thus, in essence, when Flinders and Hilda Petrie, in 1904-05, first offered the world a glimpse of the proto-Sinaitic inscriptions uncovered at Serabit el-Khadim, it could be argued that they provided scholars with an astonishing piece of evidence that this ancient Semitic script (c. 1800 BC) could theoretically be the same writing system used by the Jewish patriarchs and matriarchs. The fact that the proto-Sinaitic script’s direct descendants include the whole Phoenician/Proto-Canaanite alphabetic tradition (c. 13th to 11th centuries BC), as well as the Paleo-Hebrew alphabet (starting around the 10th century BC), significantly, provides a sort of continuum which leads us directly into the cultural realm of the ancient people of Israel and the Hebrew Bible.
Below: A beautifully executed painting showing Moses and Aaron with the 10 Commandments, by Aron de Chavez, circa 1674. Artists often depict the 10 Commandments as being anachronistically written in the Hebrew script; the paleo-Hebrew script only appears circa the 10th century BC, while the proto-Sinaitic script is much earlier, c. 1800 BC.
Credit: A painting from Aron de Chavez (Amsterdam, c. 1674). From Wikimedia Commons. File:Moses and Aaron with the 10 Commandments 1674.jpg, CC-PD-Mark.