As I am interested in historical linguistics, I have read a bit about the origins of the Hebrew alphabet. Of course most people would find the question odd. There’s a midrash that the Torah text preceded creation, one about why the Torah starts with the letter bet, and one on how the tablets with the commandmends where see-through and the inner parts of mem and samech floated. And probably more. Which are all based on the assumption that the Hebrew script has always been the same as it is now.
But there has been discoveries of Hebrew text written in a different script and there is actually even a discussion in the Talmud about the topic:
Mar Zutra or, as some say, Mar ‘Ukba said: Originally the Torah was given to Israel in Hebrew characters and in the sacred [Hebrew] language; later, in the times of Ezra, the Torah was given in Ashshurith script and Aramaic language. [Finally], they selected for Israel the Ashshurith script and Hebrew language, leaving the Hebrew characters and Aramaic language for the hedyototh. Who are meant by the ‘hedyototh’? — R. Hisda answers: The Cutheans. And what is meant by Hebrew characters? — R. Hisda said: The libuna’ah script.
(Babylonian Talmud, Sanhedrin 21b, Soncino translation)
The ‘Hebrew characters’ may refer to Paleo-Hebrew letters. This Paleo-Hebrew script developed from Phoenician script and there are archeological records that it may have been the original way of writing Hebrew until the Second temple period where it was replaced by the Ashuri ("Assyrian") script, what we know as Hebrew script nowadays (Chaim Clorfene: Finding the Original Hebrew Script, Jewish virtual library: History of the Aleph-Bet).
The reference to the "Cutheans" is also interesting. The Soncino translation that I have quoted above contains a comment that "Cutheans" refers to the Samaritans. And actually the Samaritan alphabet for writing Samaritan Hebrew is a direct descendant of the Paleo-Hebrew alphabet. The Samaritans split off from the other Israelites probably around the time of the Assyrian conquest of the Kingdom of Israel in approximately 721 BC, so it makes total sense that they would not switch to the Ashuri script but continue to write in their version of Paleo-Hebrew.
Although this timeline fits the archeological findings* (and you might think who cares how Hebrew was written a very long time ago), there is a theological problem with it. Namely, that in this setting the Torah given at Sinai would have been in a different script than the Torah we read today!! So what are we to make of midrashim, interpretations and inferences that base themselves on the letters of the Torah?
I am not qualified to give an answer, but I will end with the final words of the article that inspired this post:
My personal reflection on this subject is to avoid the mistake of thinking that if Paleo-Hebrew was the original, then it must be the holier of the two scripts. The fact is that Ezra, the father of Ashuri script, was the author of three books of the Hebrew Scriptures and worked with ruach hakodesh, a form of prophecy. The Hebrew letters that came from his hand contain some of the deepest and most mystical teachings of the Torah. These letters have sustained the Jewish people for 2500 years and will undoubtedly continue to do so in the future.
(Chaim Clorfene: Finding the Original Hebrew Script)
* In Sanhedrin 22a a second statement is brought in the name of Rabbi which basically states that the Torah was always written in Ashuri, except for a short period after the children of Israel entered the land of Israel, mixed with the locals, turned to idolatry and also adopted their script. Which was rectified by Ezra who re-introduced the original Ashuri script. Unfortunately, this does not seem to fit the archelogical evidence (Chaim Clorfene: Finding the Original Hebrew Script).