How can one persuade those who believe that Almighty God is responsible for the will of all people, even faith or disbelief, that a person's disbelief stems from their own choice and acceptance of this path, by citing God's sending of prophets as bearers of good news and as warners?

What the questioner said to his companion is the truth. Allah created man and gave him will, ability, and choice, and made him capable of both good and evil. Allah the Almighty says: "And [by] the soul and [by] Him who fashioned it and inspired it [with discernment of] its wickedness and its righteousness." (Quran 91:7-8). And He burdened him with commandments based on that. So, man acts by his choice, and Allah observes him and recompenses him for his deeds. This is supported by the saying of Sheikh Al-Albani: "The evidence from revelation indicates that man has earning, action, ability, and will, and by virtue of his disposition of that ability and will, he becomes among the people of Paradise or the Fire." And one must avoid disputing about divine decree. It must be known that the servant, his deeds, and his will are all from Allah's creation. Allah the Almighty says: "And you do not will except that Allah wills" (Quran 76:30), and He says: "While Allah created you and that which you do." (Quran 37:96).