That doesn't help the atheist case only the Anti God case.
Again if you believe there might be a God it would be irrational not to act on that and make excuses for that irrationality.
Every time I have considered the reasons given for the existence of God, I find them wanting. They seem to be the result of pure speculation, without any evidental back up whatever. Hence I would say I have acted on the possibility that God exists, and found nothing to encourage me to have a belief in any god.
On the personal level, too, I find no detectable influence that leads me to think that a god exists(indeed, my personal experiences are to the contrary), although I would not in any way suggest that my personal experiences carry any weight whatever, just as I suggest your experiences don't either. The only reason I mention this is because you seem to regard personal experiences as very important.
As I don't believe there are gods, but as I accept that it is possible that gods exist, I consider my approach to be entirely rational.