Was the Alphabet as we know it today was used at the time of Haman or was it a different Alphabet until it was re established by Ezra the scribe?

Shalom, Thank you for your question. As you can see from my previous answer to a similar question, the issue of when the alphabet we use today (called the Ashurit alphabet) was first introduced is one of debate. According to some opinions it was first used from the time of Ezra, which was after the time of Haman and the Purim story. If so, then during the Purim story the ancient Hebrew script was in use. But according to other opinions in the Talmud, the Ashurit script was always used by the Jewish people. I hope that my longer answer (to which you attached this question) will be of more help to you, and allow you to delve into the matter more deeply. Blessings.