Anonymous, just as we the Loshen HaKodesh handwritten script today which is different than the Square Script (Ksav Ashirus) we use for klei kodesh , so too was Paleo-Hebrew, which was the script used by the Yisroeilim as an everyday, easy, simple cursive script that was easily engraved in clay and stone, used at the time. The fact that they wrote in Paleo-Hebrew does not mean the Torah wasn’t given in Square Hebrew Script and that also doesn’t prove that the Torahs and mezuzos written during the First Bais Hamikdosh were not in Square Script .
The term Ksav “Ashirus” is misleading just as “Yiddish” is derived from very little “Yiddishe” (Hebrew) words, mainly it’s Old German, Slavic, and local languages where Yiddishe is spoken, so it’s original roots are not so Yiddish. In the same way, Ksav Ashirus was not adopted from the Assyrians, rather they adopted the Loshen Hakodesh script from us.