For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who by their unrighteousness suppress the truth. For what can be known about God is plain to them, because God has shown it to them. For his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made. (Romans 1:18-20)What is the form of this revelation? His eternal power and divine nature. So there are things (perceived) in this world around us that point to attributes of God which in and of themselves are not visible.
What points to God's eternal power? Those things which may suggest to us God is powerful. The size of the earth, the stars of space, the creatures of this world. Creations that speak of design.
What points to God's divine nature? Those things in this world which reveal the image of God in creation. The behaviour on animals, the behaviour of humans, love, goodness, the hatred of murder and falsehood. Attributes that speak of morality.
I have left out the distortion of these due to the Fall as this is not of God's doing. So broken design and immoral actions while in existence may not point to God directly, though they may do indirectly.
Now there may be other aspects further than design and morality that Paul is alluding to here, but these seem to me to be the 2 that are enough to convince men about God. And while there may be many proofs of God's existence, it is possible that these 2 are the most powerful.
There is another reason to suspect that design and morality are the 2 classes of evidence that Paul is referring to, further in the passage Paul states the results of denying them. Romans continues
So they are without excuse. For although they knew God, they did not honor him as God or give thanks to him, but they became futile in their thinking, and their foolish hearts were darkened. Claiming to be wise, they became fools, and exchanged the glory of the immortal God for images resembling mortal man and birds and animals and reptiles.In not acknowledging God people now sin in the areas that they deny. They reject design so they worship the designed rather than the designer and they reject morality so they act immorally but claim their actions are eumoral (morally good).
Therefore God gave them up in the lusts of their hearts to impurity, to the dishonoring of their bodies among themselves, because they exchanged the truth about God for a lie and worshiped and served the creature rather than the Creator, who is blessed forever! Amen.
And since they did not see fit to acknowledge God, God gave them up to a debased mind to do what ought not to be done. They were filled with all manner of unrighteousness, evil, covetousness, malice. They are full of envy, murder, strife, deceit, maliciousness. They are gossips, slanderers, haters of God, insolent, haughty, boastful, inventors of evil, disobedient to parents, foolish, faithless, heartless, ruthless. Though they know God's decree that those who practice such things deserve to die, they not only do them but give approval to those who practice them. (Romans 1:20-25, 28-32)
So it is possible the strongest evidence for God's existence and our obligation to him come from the existence of design and morality. These are not the only arguments that could be made for God's existence, but they are arguments that all have some appreciation of. The kalam argument (all effects need a cause) is a strong argument but it relies more heavily on philosophy and abstract logic; therefore it is less easily grasped by all people. Whereas we are forced to face the moral argument by our consciences daily, and design is apparent in many things of varying complexity which, again, we see daily.
And it is possible that the reality of design and objective morality are the aspects of the general revelation of God that is most attacked.