At the basis of the unbelievers world view we don’t find science, philosophy or similar, we simply find rejection of their creator – the God of the Bible. I’m sure that all atheists would disagree with this, however.
In the Bible we find the following in Prov 3:5: "Trust in the Lord with all your heart and do not lean on your own understanding". Unbelief is, at it’s root, a failure to believe or trust God (either willfully or unwittingly) and instead leaning on your own understanding.
The truth about God is obvious, it is clear and it is undeniable:
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. So they are without excuse. (Rom 1:19-20)
However, it is possible to start from a position of unbelief and make a compelling argument for that position. This doesn’t make that position correct, but it can make it intellectually viable to believe that point of view.
The interesting thing is that it is not our evil acts that condemn us (ironically), rather it is this simple unbelief that condemns us. Why? Because the truth is clear and obvious, and rather than submitting to the Lord and trusting Him, the unbeliever has decided that they are more authorized or qualified than God to determine reality, and they put all their trust in their own opinions (formed through the equally unbelieving opinions of others in many cases) – in other words they "lean on [their] own understanding".
As Christians, this should help us understand how we should live. If we want to worship the Lord, it is as simple as trusting Him and His word rather than our own understanding. We don’t understand everything (nobody does except the Lord), and even what we do know may be wrong, however the word of God stands as truth and stands the test of time:
All flesh is like grass, and all its glory like the flower of grass, the grass withers, the flower falls, but the word of the Lord remains forever. (1 Peter 1:24-25)
Therefore, as the word of God stands, then it is reasonable to think that perhaps this singular truth is more reliable than our own understanding.
This is the heart of faith – believing God – not just believing in God, but believing Him and submitting to His word by obeying it – even when we don’t understand why.
This is also the heart of evangelism. We are to call people not just to believe in God, but to believe God – to trust Him and submit to Him. Which is why science and philosophy fails as an evangelistic tool – all it can do is (at best) prove that God exists – it does not lead us to trust Christ at all.
As for those who do not believe scripture is clear:
They exchanged the truth of God for a lie and worshipped and served the creature rather than the Creator who is blessed forever! (Rom 1:25)
Our favourite creature is the one we see when we look in the mirror.