Is it God's fault that people cannot change since God did not choose them in the first place?
The apostle Paul anticipated that people might ask your same question. God gives us insight to your question in the book of Romans.
1. God will hold all people accountable for their sin.
Now we know that whatever the law says it speaks to those who are under the law, so that every mouth may be stopped, and the whole world may be held accountable to God. For by works of the law no human being will be justified in his sight, since through the law comes knowledge of sin — for all have sinned and fall short of the glory of God. (Romans 3:19–20,23 ESV)
In Romans 1–3, Paul explains that all men are accountable to God. God has revealed to all men that it is man’s responsibility to honor and submit to the Creator God. God has revealed Himself to man through creation, man’s conscience, and the written law. All men have failed to properly respond to God’s revelation, and they are culpable and responsible.
2. God chooses to whom He will grant mercy.
What shall we say then? Is there injustice on God’s part? By no means! For he says to Moses, “I will have mercy on whom I have mercy, and I will have compassion on whom I have compassion.” So then it depends not on human will or exertion, but on God, who has mercy. For the Scripture says to Pharaoh, “For this very purpose I have raised you up, that I might show my power in you, and that my name might be proclaimed in all the earth.” So then he has mercy on whomever he wills, and he hardens whomever he wills. (Romans 9:14–18 ESV)
God must judge and punish the sins of men. God is also loving, so God decides to extend mercy to some.
God told Moses that He has the prerogative as the Sovereign Lord to whom He grants grace and mercy. We have done nothing to merit God’s favor and grace. We have nothing to offer God to deserve mercy; the act of mercy is God’s sovereign choice. When the universe understands that God’s mercy is only based on God’s volition alone, God is glorified.
3. God cannot be blamed or faulted for withholding saving grace.
You will say to me then, “Why does he still find fault? For who can resist his will?” But who are you, O man, to answer back to God? Will what is molded say to its molder, “Why have you made me like this?” Has the potter no right over the clay, to make out of the same lump one vessel for honorable use and another for dishonorable use? What if God, desiring to show his wrath and to make known his power, has endured with much patience vessels of wrath prepared for destruction, in order to make known the riches of his glory for vessels of mercy, which he has prepared beforehand for glory. (Romans 9:19–23)
God’s creation cannot say, “God is unfair.” Paul gives an analogy that just as the potter has full right and control over how he molds the clay, God has the right and privilege to whom he can show mercy.
All of us have sinned, and we deserve God’s full wrath. Yet to demonstrate his love for us, God sent Christ to die to pay the penalty of sin for his people. God sends His Spirit to quicken man’s heart to repent and turn to God in faith.
None of us deserve God’s grace. Yet as the Creator and Sovereign God, He has the right to glorify Himself by choosing some.
Oh, the depth of the riches and wisdom and knowledge of God! How unsearchable are his judgments and how inscrutable his ways! For who has known the mind of the Lord, or who has been his counselor? Or who has given a gift to him that he might be repaid? For from him and through him and to him are all things. To him be glory forever. Amen. (Romans 11:33–36)