Did Macbeth find out that he is thane of cawdor immediately after hears the prophecy?

No, Macbeth does not find out that he is Thane of Cawdor immediately after he hears the prophecy. It takes some time for the news to reach him. In the play, Macbeth and Banquo encounter three witches who make several prophecies, including that Macbeth will become Thane of Cawdor and eventually King of Scotland. Macbeth is initially skeptical of the witches' words, but he becomes more ambitious and power-hungry as the play progresses. He eventually murders King Duncan and seizes the throne, but he is plagued by guilt and paranoia and ultimately meets a tragic end.