It was recently announced that Black Ops Cold War will officially come out November 13, and that the multiplayer reveal would be on September 9 for PS4, Xbox One, PC, PS5 and Xbox Series X. Its initial file size will take up 100GB! However, Activision have kept quiet for the Beta release, until NOW.
The Arabic PSN store put up a listing for the game, which says the open beta will begin on October 8th. Activision have said nothing official, however, this is most likely the date for the beta release.