Americanization does not begin with language (given that language is very important). Since its beginnings Israeli culture has been influenced by other cultures. The Zionist project did not provide instructions on how to operate public life, culture and language (notwithstanding the detailed vision of Herzl). Americanization was preceded by Russification, Polanization, Germanization, Arabization and Frenchification – and this is only a partial list.
Hebrew has always been influenced by other languages – Aramaic in Talmudic times, Arabic in the Middle Ages and in modern times Russian, Polish and German. In ancient times Greek influenced it and later Yiddish, Ladino and other Jewish languages.
In this linguistic playground English was a very minor player. British English during the mandate period had almost no influence except for a few slang words. American English began to have an impact in the 70’s as part of technology transfer as well as cultural content. Music, entertainment, new professions (changing the job market), the growing impact of advertising and growing consumerism of the middle classes. New technological terminologies, movies and TV programs, records and disks, computers and the Internet all served to inject American English into Hebrew.
American English has become the lingua franca of the entire world (and could now be called Globish).