"In the beginning" there was this God and we've come along later.
What's more, according to the Bible, this God: Father, Son and Holy Spirit, creates not out of need but out of generosity - not from emptiness but from fullness. Make sense?
If that's the case then we are entirely unnecessary, a profligate extravagance, a superfluous addendum, an embellishment, a flourish. We are not needed at all. We are wanted, which is nice, but it all puts us soundly in our place.
So that's the position if the God of the Bible actually exists. But... if such a God doesn't exist then, of course, we are the certain thing. The natural world (as Enlightenment people are wont to call it) is what's really real. The super-natural? Well that's, by definition, the extra thing isn't it? What we can see, hear, touch, taste and feel is rock solid. Anything beyond that is sinking sand, wouldn't you say?
Now... in a discussion between a Christian and an atheist, who has the burden of proof? Who must justify their position by bringing evidence that overwhelms the assumed 'default position' (the null hypothesis)?
If we were talking about the existence of Big Foot, we can probably all agree that those who believe in Big Foot's existence have the burden of proof. They need to bring convincing proofs or else we'll continue to hold our null hypothesis. Our null hypothesis is: Big Foot's existence is unproved and in serious doubt until further, convincing evidence is produced.
So then, why not say exactly the same about the Christian God? Why not say "The existence of God is in doubt until extraordinary evidence is produced"? Why not put the burden of proof on the Christians?
A couple of reasons off the top of my head:
1) God is not in any way like Big Foot. Big Foot (if he exists) is an extraordinary being within the created order. But God - despite how both atheists and some theists want to paint Him - is not just a super-being. The God of the Bible is the Source of Being. And the difference between a super-being and a source-of-being is not one of mere quantity. We're talking about a qualitative difference of infinite proportions.
According to Acts 17: "In Him we live and move and have our being." If Big Foot actually existed it would have no implications except for a small number of enthusiasts. God's existence changes everything for everyone. Who He is, fundamentally changes the universe we inhabit. It changes who we are - suddenly we are unnecessary-but-loved creatures of the living God. Therefore God's existence cannot be held at arm's length and discussed at a distance. When we talk about God we're talking about a reality-defining being. He defines us. And He also defines - must define - Himself.
That's the second reason why the burden of proof is not obviously with the Christian...
2) Anyone who claims that God must justify His existence is clearly not dealing with the Christian God. The great I AM is. Actually God must justify our existence! If that doesn't sound right it can only be because we're not considering the actual God of the Bible. To think of God as a potential addendum to reality is not to think of the living God.
If a person claims that God's existence is possible but requires additional proofs, they show that they are refusing to consider the reality of God. If the triune God exists then God is not the 'added thing' whose reality may or may not be granted. If the Christian God exists, we are the added thing. If the Christian God exists, He must be taken for granted as the certain reality or else we're just not talking about God, only a Big Foot in the Sky.
Who has the burden of proof? It all depends on whether God exists! If the triune God lives then of course it's our existence that must be justified, not His. The good news is that God the Son does justify our existence - He enters it, redeems it and binds it to His own existence forevermore. Jesus is not simply proof of God's existence - He's the guarantee that we exist - really and truly connected to the eternal life of Father, Son and Spirit.
But if the triune God of Scripture doesn't exist - if 'God' is merely a super-being somewhere or there is no god - then the burden of proof would lie with the theist. Because then our existence would be most fundamental and the extra thing - 'God' - would have to show itself.
So then, if someone insists that the burden of proof is with the believer, they may claim to be open-minded about the possibility of God but they have, in fact, decided the issue in advance. By setting things up in this way they have determined not to deal with the great I AM, only with a potential super-being (and only if that super-being passes the tests they set).
In other words:
No-one seeks God... Faith comes through hearing (Romans 3:10; 10:17)