Having studied the Paleo Hebrew some time ago, and having some lessons from an Israeli Hebrew Scholar on the matter, I will add this.
From the book of Exodus we read that Moses was brought up in the household of the Pharaoh. He was schooled in all the Egyptian ways, this would include religious, medicinal, mathematics, science and writing. So we must conclude that he could at least read if not write in Egyptian hieroglyphs. But this is not what the bible was written in. Further, we know that he could write, because HaShem tells him to write in a book all the words he spoke to him.
Now we all know that the Torah, the first five books, and how long they are. Even carefully with a quill and ink it would not take forty days to write out the Torah. Now today with all the rules and regulations on writing (making a copy) of the torah scroll it takes a scribe approx a year and a half to do a full torah. But he is copying, and must be sure to not make a mistake.
So even if he was not familiar with this, he could have learned it quickly as it is pictorial and he was familiar with an even more complicated form in the Egyptian hieroglyphs.
It seems that the Levites could also write, they were to write certain things in a book, and one of the commandments involves writing the crime on a piece of paper (this has to do with infidelity if I remember correctly), and Israel itself was commanded to write the commandments on the mezzuzah. There were ketubahs and bills of divorcement which were written documents.
Before they entered the promised land they were to set up stones and write all the commandments upon them.
So writing, in this ancient language must have been well known. Some say it only dates to the 10th century, during King Davids time but it must go further back than that. And the fact that it is still in use today by the Samaritans, believing they have the 'true Torah', is also telling.
Paleo Hebrew is closely related to the Phonetician alphabet but is read differently.
Then there is Proto Sinaitic which was used during the same time as Egyptian hieroglyphics and is considered by some to be the true alphabet. This could be the Alphabet that was passed down with the Hebrew language at Babel. This is seen by some historians as the alphabet that preceded the Phonetician, which many alphabets derived from.
The proto-Sinatic is more pictorial than the Paleo we know of. For instance for the letter aleph, there is a bulls head of no mistake. From this derived the symbol which today looks like our Arabic letter 'A' set on it's side. The Moabite language is also very similar.
These symbols for letters seems to have been used for many a century, even into the common era on some coins.
Even some of the DDS are written in a form of this pictorial paleo Hebrew.
Pictured below is a Hasmonean coin which I photographed at the exhibit from Israel to the US of the Dead Sea Scrolls. On it you can clearly see the Paleo Hebrew.
This coin is Bronze, and minted in Jerusalem It is dated to the time of John Hyrcanus I, 135-105 BCE
John Hyrcanus I was the nephew of Judah Maccabee. Under his rule the first coins were struck, symbols of the newly established sovereign Jewish state ruled by the Hasmonean dynasty.
On the reverse side of this coins is a double cornucopia with a pomegranate atop a priestly scepter between horns.
The side showing reads: "Yehohanan the High Priest and Council of the Jews"
