Does God exist?
NO. God does not exist until/unless evidence of his existence is presented. This evidence will be data that points to the conclusion of his/her existence, in spite of prejudices or preconceptions of the persons looking at the data.
But, but what if? Isn't there a possibility?
Sure, but is it reasonable? I learned this while serving on many jury duties. There is a murder. A dead body is outside of a bar with a knife in it's back. A trail of blood lead to an apartment, where a suspect is found with blood on his hands and clothes that matches the victim's. A receipt is found for the purchase of the hunting knife. Several witnesses in the bar state that the suspect and the victim were arguing and fighting and death threats were uttered. The suspect confessed to the killing.
But wait, what if space aliens came and hypnotized everyone and killed the man and planted the knife? This is unlikely, but possible, anything is possible, so you must acquit.
Yes, theoretically this is possible, but is it REASONABLE?
The same thing applies to gods. Sure, anything is possible in the human imagination, but is god reasonable to think to exist? I say "No", and I do not say that gods do not exist, but I THINK that they do not exist with the same confidence that I think that vampires, werewolves, ghosts, poltergeists and space aliens who stage murders do not exist.
Until, unless there is evidence, God does not exist.
Neither can God be rationalized into existence, This art is called apologetics.
It is noteworthy that there are zero arguments for the existence of god that bring forth traditional evidence. Contemporary gods are all mysterious, hidden and unknowable. They all have one thing in common, they are just not around. Things like faith, argument from ignorance and personal incredulity are invoked. Of course, god could end all of this in a blink of an eye. Why doesn't he? The answer is obvious.