No, a choice has to be free to be a choice. A "choice" with a predtermined outcome is not a choice.
All men "have a choice." And all men choose poorly unless and until God regenerates them
Then it's not a choice.
That's what the Bible tells us and I believe the Bible
The Bible also says that God desires all men to be saved. Obviously you don't believe that part.
Context counts. From Calvin's Commentary on 1 Timothy 2:4...
Hence we see the childish folly of those who represent this passage to be opposed to predestination. "If God," say they, "wishes all men indiscriminately to be saved, it is false that some are predestined by his eternal purpose to salvation, and others to perdition." They might have had some ground for saying this, if Paul were speaking here about individual men; although even then we should not have wanted the means of replying to their argument; for, although the will of God ought not to be judged from his secret decrees, when he reveals them to us by outward signs, yet it does not therefore follow that he has not determined with himself what he intends to do as to every individual man. But I say nothing on that subject, because it has nothing to do with this passage; for the Apostle simply means, that there is no people and no rank in the world that is excluded from salvation; because God wishes that the gospel should be proclaimed to all without exception. Now the preaching of the gospel gives life; and hence he justly concludes that God invites all equally to partake salvation. But the present discourse relates to classes of men, and not to individual persons; for his sole object is, to include in this number princes and foreign nations. That God wishes the doctrine of salvation to be enjoyed by them as well as others, is evident from the passages already quoted, and from other passages of a similar nature. Not without good reason was it said, "Now, kings, understand," and again, in the same Psalm, "I will give thee the Gentiles for an inheritance, and the ends of the earth for a possession." (Psalm 2:8-10.) In a word, Paul intended to shew that it is our duty to consider, not what kind of persons the princes at that time were, but what God wished them to be. Now the duty arising out of that love which we owe to our neighbor is, to be solicitous and to do our endeavor for the salvation of all whom God includes in his calling, and to testify this by godly prayers. With the same view does he call God our Savior; for whence do we obtain salvation but from the undeserved kindness of God? Now the same God who has already made us partakers of salvation may sometime extend his grace to them also. He who hath already drawn us to him may draw them along with us. The Apostle takes for granted that God will do so, because it had been thus foretold by the predictions of the prophets, concerning all ranks and all nations.""Lastly, he demonstrates that God has at heart the salvation of all, because he invites all to the acknowledgment of his truth. This belongs to that kind of argument in which the cause is proved from the effect; for, if "the gospel is the power of God for salvation to every one that believeth," (Romans 1:16,) it is certain that all those to whom the gospel is addressed are invited to the hope of eternal life. In short, as the calling is a proof of the secret election, so they whom God makes partakers of his gospel are admitted by him to possess salvation; because the gospel reveals to us the righteousness of God, which is a sure entrance into life.