Your overarching problem is that you believe man is capable of reconciling himself to God in his natural estate. That incrementally he will come to a fuller understanding of God and reason his way to faith in God. But this is impossible according to the scripture. Romans 8:7-8 teach that the carnal mind is enmity against God. It is not subject to the law of God and cannot be subject to it. From this estate, it is impossible to please God. But you proffer that such a one will recognize the authority of God, transfer that recognition to the Son, and obey God. The word of God says that cannot happen. The gospel is foolishness to such folks and the gospel is not the power of God unto salvation for them. Even if they make a pretense of religion, they deny the power thereof.
If you truly want to understand the depravity of man and his helplessness before God, spend some time meditating on Romans 8.
According to you this my problem, and I understand why you think this. And I think you are misreading His Word and the 1Cor2 verse you are referencing, at least in part. Thus, I think it's you who has the problem.
In Paul's mind and throughout his writings, especially Romans, is a kind of duality in men - there are men of faith who believe God and unrighteous men who in early context are the not men of faith who reject God. There is also his perspective that even though there are men like himself who believed YHWH - or had faith in YHWH (as Hebrews 11 tells us) - and who lived blamelessly, righteously under law, under sin, from God's ultimate perspective of perfect righteousness and holiness, all men, both Jew & Greek, men of faith and unrighteousness men, need Christ and His Righteousness from God. This is what Paul is building in Rom1 that sets the course for the rest of the document.
When you read Rom8, which is instruction to believers - men of faith in Jesus is YHWH's Christ - in living the spiritual life of a man of faith - what he says about the fleshly mindset does not negate the fact that there have been Jews for centuries living pursuant to God's Law with its sacrificial system for dealing with sin(s) and there are Gentiles who showed the work of the law in their hearts with functioning consciences. Paul has also just come out of Rom7 explaining how the Law had been instructing re: sin and making him able to perceive the struggle going on inside him as a man who desired to live as God willed. Paul will bring in the concept of the Remnant from the Hebrew Scriptures to go along with this and the Remnant was of OC men who did not bow in
obeisance (same word Jesus used emphatically in John4 re: who God is seeking) to idols but lived albeit
imperfectly in belief in God.
The problem IMO with this view of depravity that you share with TULIPism is that it works very hard to negate the truth that there have been men of faith from Abel on. These are men and women of Gentile and Hebrew heritage throughout history and the message of belief in God has been progressive and has been believed since the Garden by people before Jesus was sent.
So, I do not find it difficult to see in Scripture how some of the believing Remnant easily transitioned from belief in YHWH to being convinced by God and His people that Jesus was the God promised Messiah whom they were anticipating for centuries. Nor do I see it as impossible, as others do, to transition from belief in God to belief in His Son especially with His Spirit functioning in the world, His Word being in most of the world and having been so for millennia, consciences working to give a sense of good & bad & judgment, and other such factors, including living a life over time in a world that one can realize is an absolute mess while having in our hearts a sense of eternity - something better and greater than this catastrophe we're living out now - including death that just does not make sense if one believes in the Creator of Rom1 and the powers He has.