(All citations LEB)
The word "know", ginosko, implies an experiental knowledge. It is a reference to having some kind of revelation of God. This revelation of God is provided through creation. The specific attributes called out here are
God's eternal nature - in contrast with man's fleeting life.
God's diety - in contrast with man's status as created being who is living in God's order
God's divine nature - in contrast with man's carnal life.
Absolutely none of this has to do with "being a good person". Neither is this really an apologetics argument trying to prove that God exists, as that would be obvious to people in Paul's day. It is all about recognizing man's position vis-a-vis God. It is about man needing to be humble and honor God in his heart rather than be vain in his heart. How would man be vain and refuse to honor God even if he had never read a scripture? By insisting in his own mind that man could do better than the order that God created. That is, judging for himself good and evil in his own mind, and thus deciding that the created order is (morally) wrong somehow or can be (morally) improved to conform to man's own imagination.
For from the creation of the world, his invisible attributes, both his
eternal power and deity, are discerned clearly, being understood in
the things created, so that they are without excuse.
So man views himself as a little god, existing in the mind, sitting on a little throne in the mind, making pronouncements as to what is right and what is wrong, pointing an accusing finger at this or that and decrying it as being evil or praising it as being good. There is a little snake, or accuser, in our heads doing that. And man listens to that accuser, living out his life according to what is right in his own eyes.
So the emphasis here is that God expects that being confronted with the created order, which reveals God's divinity, his eternal nature, and his diety - that man abandon the vain imaginations of his own mind and recognize that he is in error and in need of repentance.
This repentence should take the form of recognizing that only God can judge good and evil, being thankful to God for the created order as it exists rather than critiquing it according to man's imaginations.
For although they knew God, they did not honor him as God or give
thanks, but they became futile in their reasoning, and their senseless
hearts were darkened.
But most men do not do this, they continue to turn inward and follow their own inner voice which is the voice of the Dragon.
Trust in the Lord with all your heart,
and do not lean on your own understanding. In all your ways acknowledge him,
and he will make straight your paths.
and also Prov 14.12:
There is a way that seems right to a man, but its end is the way to
And so God abandons them to their own lusts, he darkens their mind, and allows them to worship each other, first and foremost themselves, but also their neighbors, and then, in mockery of man's foolishness, various animals, and finally inanimate objects as a type of final insult to man's humiliation, which is God's just response to man trying to pretend to be god in his own vain mind. God's response to man trying to climb above his station is to humble him by bringing him to the bottom.
Who among you is in fear of Yahweh, obeys the voice of his servant?
Who walks in darkness and has no light, trusts in the name of Yahweh
and depends on his God? Look! All of you are kindlers of fire, who
gird yourselves with flaming arrows. Walk in the light of your fire,
and among the flaming arrows you have kindled! You shall have this
from my hand: you shall lie down in a place of torment.
Just as God curses those who try to do good by raising up evil within them to thwart them (Rom 7.21), so God thwarts man's efforts to elevate himself to be God by making him a slave of things lower in creation than man is.
Claiming to be wise, they became fools, and exchanged the glory of the
immortal God with the likeness of an image of mortal human beings and
birds and quadrupeds and reptiles. Therefore God gave them over in the
desires of their hearts to immorality, that their bodies would be
dishonored among themselves, who exchanged the truth of God with a
lie, and worshiped and served the creation rather than the Creator,
who is blessed for eternity. Amen.
Note that here we are talking about fallen man. The spiritual man has the mind of Christ and is able to judge all things (1 cor 2.15), but that's because the spiritual man is not relying on his own understanding but has taken every thought into captivity that exalts itself above God (2 cor. 10.5), and then the mind of Christ reveals to him all things.