Would concede in the face of conclusive evidence. There is no reason as to why not.
To us, the existence of God is just another claim that many delusional people believe in. No conceivable evidence has been given, ever. The so called "evidence" that any religious person has ever given in the known history of mankind have been either proven false or deemed unfit using logic. Usually, they are just another assertion, fallacious arguments, or personal revelation.
But it will never be evidence, it'll always be something religious people believe. You all think we're closed minded, but if we saw evidence of either a god, or evidence that we were wrong, then we would start to go onto your side. You just have to have evidence, not something you made up. And saying various locations in the bible are real doesn't count as evidence, that's like saying "Harry Potter is in England, and England is real, so Harry Potter must be real!".
If the evidence is legitimate evidence, we will not call it false. Come up with some evidence first.
If the evidence is verifiable and legitimate, we would be hypocrites not to accept it. The reason we have not accepted the evidence thus far is because it has not been legitimate or has not been deemed logical. If the evidence is not based on "faith" and "belief" but scientific findings, we would have to accept it as truth.
As others have stated, once evidence for the reality of religious conjecture is brought forth, atheists will certainly admit the truth in it. Up to the current time, however, this has never been done. The majority of arguments from the religious are couched in terms of "belief" and "faith" which are not, and cannot be measurements of truth or fact to the degree that we consider scientific findings truthful and factual.
If theists had any actual objective, verifiable evidence that a god existed then of course we would accept it. But they don't- not a shred. No one in history has ever been able to prove a god of any sort existed, much less their particular variant. There have been nothing but subjective testimonies and a lot of logical fallacies.
What evidence is there so far? ''I believe he exists'' WOA SUCH EVIDENCE, no, by that logic ''I believe the flying spaghetti monster exists'' would also be enough evidence.
Facts are facts, religion has no provided ANY factual evidence on the existence of any god therefore it's logical atheists don't believe you.
Religion is based upon faith. Fanatical theists will not change their minds on the existence of God no matter what evidence for the contrary is presented to them. The opposite is true for ideas based on evidence.
Most atheists do not believe in God because there is overwhelming evidence that God is extremely unlikely and unnecessary in order for our world to exist as it does. This belief is based upon empirical proof or logical ideas. If proper proof for the existence of God can be produced then ideas will change.
As an atheist, I think there is plenty of evidence for religions. Unfortunately, it is not good evidence. Most religious people I talk with don't understand that all evidence is not equal. Anecdotal evidence is evidence, it just isn't terribly good evidence. The same goes for evidence from personal experiences and revelations. They don't hold a candle to verifiable, repeatable, testable evidence collected under controlled conditions.
There is a distinct difference between a religious person and an Atheist. For Religion, "Believing is seeing." For an Atheist, "Seeing is believing." If Jesus, God, Shiva, Buddha, whatever your deity came down and started performing miracles that would be impossible to perform, even with today's technology and stage craft, I am sure some people would turn. In fact, some Atheists are very open to the idea of Religion, it's just that it doesn't have them entirely convinced yet.
How do you expect to prove something to an Atheist? Most of them prefer evidence. And most evidence, is scientifically based. Furthermore, science believes in what it's tools can measure or calculate.
Science have no tools, at least today, to measure religion. Religion is a concept (not something physical), and most of the claims made by religion involves non-physical things. Hence, science doesn't measure non-physical things.
Somebody may say, or in fact, even if a group of people said they had left their bodies, visited heaven, and came back, well all of that is still not measurable. Metaphysical bodies cannot be measured by physical scientific instruments.
Sure, the atheist can set up logical tests to see if the whole group was just making stuff up. But, just because a group of people happened to be giving out the same information, or even giving out valid information, all that proves is that the group isn't lying. And if the group didn't lie about seeing a Heaven, that still doesn't prove a Heaven exist. Because to the Atheist, it just has to be something else that made them all saw Heaven; must be drugs, time of day, brain tricks, etc.