Yes and no.
No, we cannot change God’s mind. God has a plan and He will fulfill His purposes. Isaiah 46:9-10 (NET), “Remember what I accomplished in antiquity! Truly I am God, I have no peer; I am God, and there is none like me, who announces the end from the beginning and reveals beforehand what has not yet occurred, who says, ‘My plan will be realized, I will accomplish what I desire…’”
Additionally, when God gives a promise, He never withdraws it. Romans 11:29, “For the gifts and the call of God are irrevocable.”
Therefore, on some issues, God cannot and will not change His mind. Even “if we are faithless, he remains faithful— for he cannot deny himself..” 2 Timothy 2:13.
Yes, we can change God’s mind when God sees that His goals will be reached using a different path. For example: while Moses was receiving the 10 Commandments and the Law, Israel was worshipping the golden calf. God was very angry and said He was going to destroy the nation. God would still fulfill His promises to Abraham through Moses (an Israelite). But Moses pleaded with God to let the nation live. And God honored Moses’ request.
Exodus 32:9-14 (NIV), “‘I have seen these people,’ the LORD said to Moses, ‘and they are a stiff-necked people. Now leave me alone so that my anger may burn against them and that I may destroy them. Then I will make you into a great nation.’ But Moses sought the favor of the LORD his God. ‘LORD,’ he said, ‘why should your anger burn against your people, whom you brought out of Egypt with great power and a mighty hand? Why should the Egyptians say, It was with evil intent that he brought them out, to kill them in the mountains and to wipe them off the face of the earth? Turn from your fierce anger; relent and do not bring disaster on your people. Remember your servants Abraham, Isaac and Israel, to whom you swore by your own self: I will make your descendants as numerous as the stars in the sky and I will give your descendants all this land I promised them, and it will be their inheritance forever.’ Then the LORD relented and did not bring on his people the disaster he had threatened.”
God invites us to reason with Him. Isaiah 1:18, “Come now, and let us reason together, saith the LORD…” Sometimes, we may reason with God in prayer and ask for something. But when we do, we should always follow Jesus’ example. In the Garden of Gethsemane, He prayed, “O My Father, if it is possible, let this cup pass from Me; nevertheless, not as I will, but as You will.” Matthew 26:39