Technically, the proto-Sinaitic script is an abjad, with the Greek alphabet being the first true alphabet (symbols for both consonants and vowels).

Proto-Sinaitic/Phoenician can be described as the “first alphabetic system,” Greek the “first true alphabet.”

Fun fact: Greek is the world’s oldest recorded living language.

The Greek alphabet has been in use for approximately 2,800 years; previously, Greek was recorded in writing systems such as Linear B and the Cypriot syllabary.

Canaanite and its abjad have been in continuous use, in various versions, for more than 2,800 years. It's true there's no Linear B.