Well, if prayer doesn't change (at the least) God's actions, then why pray? And If you pray, believing that prayer changes things, then what does it change?
I think I know why some people doubt that prayer changes God's will. They believe His will cannot change because He can't change. A perfect being doesn't need to change.

But to say that prayer won't change God's will is to have a limited view of that will. What is God's will? A monolithic structure? Is God tied to only one way of accomplishing His purposes?
In his wonderful, concise analysis called The Will of God, Leslie D. Weatherhead makes more sense on this issue than most writers. He says the will of God h
God's original intent (will) was that mankind live in a perfect paradise in complete harmony with Divinity. But Satanic evil, along with man's sovereign choices, hijacked that will.
So now God works from His "circumstantial will" - His will as adjusted within a universe now corrupted by toxic evil.
As an example, Weatherhead mentions illness. Why do we fight with all our prayers and medical skill against illness, and then claim it was "God's will" if the person dies? Were we fighting God's will all along?
It was never "God's will" that the world be swallowed up in sickness, death, suffering and evil, but now that it has been, His will works to reverse the curse.
Simple example: King Hezekiah became ill (not God's intentional will from the beginning) and prayed. He was healed (God's circumstantial will). If he had not prayed, he would not have been healed.(See 2 Kings 20).
God's "will" waited on Hezekiah's will. When he made his choice to pray, God's will acted.
Yes, God's "circumstantial will" - in which we now exist - can be changed by prayer... by prayers that change His working in particular situations where humans have a choice.