There are two schools of thought on that:
1. Many atheists are, in fact, open to possible evidence - provided that its sufficiently compelling and unambiguous. (Lack of ambiguity is rather crucial. A beautiful sunset can be offered as evidence of god. But it could also just be the physics and psychology of pretty colors that a natural Universe produces.) The clichéd example of compelling evidence is the 600ft Jesus descending through the clouds, accompanied by angels and heavenly choir music. Sure, this could be a hallucination or aliens whove done their homework. But a number of atheists agree that such a sight would lend impressive, provisional credence to the (Christian) god hypothesis.
2. On the other hand
there are atheists who outright reject any possibility of god. But this is not close-mindedness to evidence in the typical sense. Rather, their notion is that no coherent or non-self-contradictory definition of god has ever been produced. So its analogous to the claim that square circles exist. Based on the understood definitions of square and circle, its not close-minded to repudiate a concept thats - essentially - a nonsense phrase. And for some atheists, god is equally nonsensical/incoherent; and can be dismissed for that reason.
The "what sort of evidence would it take to convince you?" discussion is very vital and gets to the crux of the issue.
The thing is that because of the nature of the claim that god exists, it may very well be impossible to demonstrate. Because of the nature of what god is (in monotheism, literally the most powerful being in the universe, the creator of everything), it is unfalsifiable.
Consider - The 'best case scenario' alternate universe (using christianity as an example).
There is not only historical verification that Jesus Christ existed, but that the 'miracles' actually happened, verified independently across multiple sources. We are as certain that Jesus Christ turned water into wine as we are that George Washington existed.
Okay, what then?
"He turned water into wine, therefore he has to be the most powerful being in the universe (and is his own son)".
Do we believe who he says he is, because he can do extraordinary things?
The issue is that practically any alternate hypothesis you can think of would require LESS assumptions, than assuming that he has to be the most powerful being in the universe.
Maybe he's an undiscovered split off from humanity, an 'X-Man', who is not necessarily lying about who he is but has simply become deluded into thinking he's the son of god.
Maybe he's an alien.
Maybe he's a time traveller with access to technology we can't yet imagine.
All of these are extraordinary claims, sure, but are they any MORE extraordinary than the claim "he is the most powerful being in the universe - he is the creator of everything".
An alien, would at least be a natural explanation.
It would be feasible in such a 'best case scenario' universe that there would be competing groups arguing over just who or what influenced the events in the bible. It would even be feasible that there would be skeptics that don't agree with either the theists or the alienists and take a position that one explanation may be more likely than another, there may be other alternative hypothesis still, but there is no real conclusion.
Okay.
How could god convince me he's real?
God could instantly fill me with certainty that he is real. Direct mental realization with no doubts.
What then?
How would I then be able to convince others? How would I be able to differentiate myself from someone that was simply deluded? Likewise if I had a personal vision of 400ft god. I simply wouldn't be able to objectively convince anyone that the experience was genuine.
God. Is. Unfalsifiable. Religious arguments for the existence of god are futile, even in the 'best case' universe.
And,
we don't live in the best case universe. We live in a universe in which faith healing is dangerous because it doesn't work, in which people that claim to be psychics fall apart at the merest pressure from scepticism, in which the evidence that Jesus even existed at all is weak (which some of you may have seen me deal with recently) never mind that he performed the miracles that its claimed he performed, we don't go around firing spells at each other like in Skyrim or Harry Potter... we live in a universe in which naturalistic explanations are parsimonious, in which the scientific method has made it possible to live well beyond the average life expectancy of our desert tribe ancestors who were afraid of demons causing disease, in which people are much more literate than they were in the middle east 2000 years ago...
The most simple explanation for the stories of the bible is that they are just stories and nothing more. That's the universe we live in. That people state with such certainty, and arrogance, that if you don't believe as they believe based on this book then your soul is doomed for eternity... is pathetic, its an utter embarrassment to our progress.