Hi InquisitiveAgnostic,
'A disbelief in God and a knowledge of its non-existence' is an impossiblity, as no-one can verify the existence of nothing.
The other problem with this statement is the apostle Paul's statement of the obvious in the wake of his warning about rejecting truth.
Here is the warning:
'[For] the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who hold the truth in unrighteousness'.
What that sentence means is, God is angry with those who exercise ungodliness and unrighteousness, while knowing better. By 'knowing better' I mean, they have a concept of the absolute standard by which they are being judged, even without being formally told. You might like to argue about what people can 'know', but I don't think Paul's words need any defence, because, as I said, he's stating the obvious. Here it is:
'... That which may be known of God is manifest in them; for God has showed it to them. For the invisible things of Him from the creation of the world are clearly seen, being understood by the things that are made, even His eternal power and Godhead; so that they are without excuse.'
Paul goes on to explain God's reasoning for His wrath:
'... When they knew God, they glorified him not as God, neither were thankful; but became vain in their imaginations, and their foolish heart was darkened'.
Words in blue taken from Romans 1, King James Bible.
The thing you have to notice is, that people begin with knowledge of God, but if they don't respect that knowledge properly, the result of laying it aside is the operation of certain spiritual laws.
What people don't seem to realise is, that acknowledging God as He deserves to be acknowledged - acknowledging truth as truth with appropriate responses to the truth revealed - being thankful for God's revelation of Himself in creation and His provision for mankind, and for knowing Him more - also triggers certain spiritual laws; laws which lead to life itself and the increase in understanding of God and His interests. One of His main intentions is to bless His obedient children. This may explain why He will not bless His disobedient children.
The apostle Paul has more to say about this contrast in Ephesians 2:1 - 3. John 3:16, 17, 18, 19, 20. 2 Corinthians 4:3, 4, 5, 6. What is needed for men who have been blinded by darkness and evil practices, is that they turn from darkness and come to the light of God - His life in Christ Jesus - to receive spiritual sight to be able to 'see' the reality of God's realm, and also be transformed by obedience and a regenerated mind.
Hebrews 11:6 is not circular reasoning. God has revealed Himself through His huge creation, and unbelief is as much of a choice as belief.