I found this drasha on the Daf Yomi Notes for Megillah 16:
The Gemora relates that Achashverosh ordered Haman to get Mordechai,
dress him in the royal garments and lead him through the city on the
king’s horse proclaiming, “Thus shall be done for the man whom the
king wishes to honor.” Haman located Mordechai teaching his students
the laws of kemitzah (scooping the flour for the mincha offering).
Rashi states that this occurred on the sixteenth of Nissan, the day
the korban omer is offered in the Beis Hamikdosh.
The Maharal explains the connection between the omer offering and the
story of Purim. The Omer offering reveals the miracles that are hidden
inside of nature. By bringing the first grain to the Beis Hamikdosh,
we are demonstrating that even the nature of the world is governed by
Hashem. This was the method used to overcome Haman. The miracles were
concealed from the human eye. The means to conquer Haman and Amalek is
by exposing the concealed miracles, thus confirming that all which
appears natural is controlled by Hashem.
In summary, based on Maharal's explanation, G-d could not have gotten rid of Amalek for us.
See the "Daily Mashal" near the end of the linked article for further explanation and other views on this. I could only excerpt a section!