Before Hebrew used its current alphabet (אבג) which was adopted from Aramaic, it used the Paleo-Hebrew alphabet (𐤀𐤁𐤂), a regional variant of Proto-Canaanite and virtually the same as Pheonician (which is the origin of the Aramaic, Greek, Latin, Cyrillic, Armenian, Anatolian alphabets and others).
I really think it should make a comeback, it's a cool script and somehow both older than modern Hebrew but also more similar to other scripts like Latin.