So you have:
1. Examples from Genesis to Revelation with absolutely no indication that unregenerated man had to be regenerated in order to believe.
2. Numerous verses that show that God is not the direct cause in making men choose Him or take positive steps toward Him.
3. Scripture verses proving that fallen man still retains the ability to choose God by telling him to do so. God tells unregenerate man to choose Him.
4. Numerous Scripture verses proving that fallen man still retains the ability to choose God by telling him to seek Him.
5. Numerous Scripture verses proving that fallen man still retains the ability to know God by telling him to turn to Him and to know Him.
6. Numerous Scripture verses proving that fallen man still retains the ability to choose God by telling him to trust God. In order for God to tell man to do this, unregenerate man must have the God-given ability to do so.
And then you have,
7. Scripture proving that fallen man retains the ability to choose God by telling man to choose to come to Him. In order for God to tell man to do this, unregenerate man must have the God-given ability to do so.
Isaiah 55:1-7
Come, all you who are thirsty, come to the waters; and you who have no money, come, buy and eat! Come, buy wine and milk without money and without cost. 2 Why spend money on what is not bread, and your labor on what does not satisfy? Listen, listen to me, and eat what is good, and your soul will delight in the richest of fare. 3 Give ear and come to me; hear me, that your soul may live. I will make an everlasting covenant with you, my faithful love promised to David. 4 See, I have made him a witness to the peoples, a leader and commander of the peoples. 5 Surely you will summon nations you know not, and nations that do not know you will hasten to you, because of the LORD your God, the Holy One of Israel, for he has endowed you with splendor." 6 Seek the LORD while he may be found; call on him while he is near. 7 Let the wicked forsake his way and the evil man his thoughts. Let him turn to the LORD, and he will have mercy on him, and to our God, for he will freely pardon.
Micah 4:2
Many nations will come and say, "Come, let us go up to the mountain of the LORD, to the house of the God of Jacob. He will teach us his ways, so that we may walk in his paths."
Matthew 8:10-12
"I tell you the truth, I have not found anyone in Israel with such great faith. 11 I say to you that many will come from the east and the west, and will take their places at the feast with Abraham, Isaac and Jacob in the kingdom of heaven. 12 But the subjects of the kingdom will be thrown outside, into the darkness, where there will be weeping and gnashing of teeth."
Matthew 11:28-29
Come to me, all you who are weary and burdened, and I will give you rest. 29 Take my yoke upon you and learn from me, for I am gentle and humble in heart, and you will find rest for your souls.
Matthew 16:24-25
If anyone would come after me, he must deny himself and take up his cross and follow me. 25 For whoever wants to save his life will lose it, but whoever loses his life for me will find it.
Matthew 19:14-15
Jesus said, “Let the little children come to me, and do not hinder them, for the kingdom of heaven belongs to such as these."
Matthew 19:21-24
Jesus answered, "If you want to be perfect, go, sell your possessions and give to the poor, and you will have treasure in heaven. Then come, follow me." 22 When the young man heard this, he went away sad, because he had great wealth. 23 Then Jesus said to his disciples, "I tell you the truth, it is hard for a rich man to enter the kingdom of heaven. 24 Again I tell you, it is easier for a camel to go through the eye of a needle than for a rich man to enter the kingdom of God."
Matthew 22:3
He sent his servants to those who had been invited to the banquet to tell them to come, but they refused to come.
Luke 6:47-49
I will show you what he is like who comes to me and hears my words and puts them into practice. 48 He is like a man building a house, who dug down deep and laid the foundation on rock. When a flood came, the torrent struck that house but could not shake it, because it was well built. 49 But the one who hears my words and does not put them into practice is like a man who built a house on the ground without a foundation.
John 7:37-38
"If anyone is thirsty, let him come to me and drink. 38 Whoever believes in me, as the Scripture has said, streams of living water will flow from within him."
1 Timothy 2:3-6
This is good, and pleases God our Savior, 4 who wants all men to be saved and to come to a knowledge of the truth. 5 For there is one God and one mediator between God and men, the man Christ Jesus, 6 who gave himself as a ransom for all men-the testimony given in its proper time.
Hebrews 7:25
Therefore he is able to save completely those who come to God through him, because he always lives to intercede for them.
Hebrews 12:22-24
But you have come to Mount Zion, to the heavenly Jerusalem, the city of the living God. You have come to thousands upon thousands of angels in joyful assembly, 23 to the church of the firstborn, whose names are written in heaven. You have come to God, the judge of all men, to the spirits of righteous men made perfect, 24 to Jesus the mediator of a new covenant, and to the sprinkled blood that speaks a better word than the blood of Abel.
James 4:4-10
You adulterous people, don't you know that friendship with the world is hatred toward God? Anyone who chooses to be a friend of the world becomes an enemy of God. 5 Or do you think Scripture says without reason that the spirit he caused to live in us envies intensely? 6 But he gives us more grace. That is why Scripture says: "God opposes the proud but gives grace to the humble." 7 Submit yourselves, then, to God. Resist the devil, and he will flee from you. 8 Come near to God and he will come near to you. Wash your hands, you sinners, and purify your hearts, you double-minded. 9 Grieve, mourn and wail. Change your laughter to mourning and your joy to gloom. 10 Humble yourselves before the Lord, and he will lift you up.
2 Peter 3:9
He is patient with you, not wanting anyone to perish, but everyone to come to repentance.
Revelation 22:17
The Spirit and the bride say, "Come!" And let him who hears say, "Come!" Whoever is thirsty, let him come; and whoever wishes, let him take the free gift of the water of life.
Anyone, everyone, whoever, adulterous people, the weary and burdened, and even those who ultimately refuse, are all told to come! They would not be told to do so, if they did not have the ability.
Again, there is no suggestion of it not being possible for unregenerate man to come to Him.