There are external, physical, examinable miracles. If you study them using forensic science, you will see where the physics are broken in this object and that it literally cannot exist under standard theory, but there it is, this object - a real miracle.
These miracles are not freebees. They all come wrapped in an informational package - they are instructive miracles. The miracle is there to be a miracle, and the fact of the miracle is there to make you look at the informational package.
All of these miracles - every one of them - has specific religious content. All of the miracles but two are Catholic. All of the miracles but one are Christian. That fact itself is informative. There is an argument from presence and from absence.
If you want God's existence, and Christian nature, revealed to your own eyes through objects anybody can study, it can be done. But nobody will go down that path unless he needs to.
Faithful Christians don't want to go there, and atheists don't either: prove God, and prove that God is a specific way, and you can't then wriggle off the hook - you HAVE to accept it. Best, then, not to see and say you don't need it. That's fine.
What isn't fine, and where I do have to object and intervene, is when the decision not to look becomes a foolish denial of the existence of such things. They do exist. They can be examined. If one chooses not to look at them, it is not because one is either too wise or too smart for that. Rather, it is because one prefers to remain ignorant of it.
I choose to remain ignorant of things all the time. Sports scores, the rules of cricket, various computer programs - the world is full of information I could learn, but choose not to because I don't want to invest the time. For many, the scientific study of the physical miracles falls in that category. And that's fine, that's a choice. But to assert in ignorance that such things don't exist at all, or are figments of the imagination, is a lie. They do, and they're not.
Do not assume too much. You're "sure" that everyone who believes in things strongly enough will have "similar stories". But in fact they don't. And there are people like Paul, or like me, who quite strongly did NOT believe in something, who then got tackled by reality and had their eyes forced open by superior force. After that they had no choice but to accept the reality of what they had come unwillingly to know.
When it comes to God, you're not in command. He can come in and force you to acknowledge his existence, and force you to reject the whole path of your life before that. Look what he did to Paul! He broke Paul, blinded him, humiliated him, forced him to be dependent on the very people he was going to torture. He forced Paul, by reality, to acknowledge in an instant that the religion by which he had sworn, and by which he enthusiastically made his living, was false and wrong, and the religion he hated most was, in fact, true. And he forced him - on pain of blindness, to go and put himself under the tutelage of the very people that a moment before he had despised.
Essentially, God took the cur, Saul, to the spot of filth that Saul had made on the rug, rubbed Saul's nose in it, and threw him out in the dark for a few days to suffer. He BROKE Saul. He broke his reputation - thereafter Paul would be detested by Jews, and beaten and at risk of his life, and distrusted by many, many Christians, who did not forget what Saul had been, and who did not trust his conversion. He left Paul physically crippled and promised Paul that He would make Paul suffer going forward. Paul would carry the message, and PART OF that message would be the ongoing example of Paul's continued suffering. Paul did it willingly, because he saw that he was wrong. Had he refused, God would have left him blind, to starve to death without Christian help. And then he would have thrown him into the fires of Hell at final judgment for the murder of so many Christians.
God was not nice to Paul at all. He put Paul through hell, as an example, BECAUSE Saul had put Christians through hell. Paul's reward was in the afterlife, not this one. And Paul knew it, and accepted his fate as deserved, because it was.
You want to believe. If God reaches out of the air and grabs you, then you know. And then what? Then you can't go back to not knowing and not believing, not ever. Because if you try, then you know full well you are being Judas, and then as the disasters pile up in your life, you will know why. God will not be mocked. If he takes the trouble to come out of the universe and space and time to look at you, mortal creature, straight in the face and say "HERE I AM", then YOU are stuck for life, and you're stuck following something you never wanted to follow, and accepting the truth of things you don't want to believe. And you know that - your wish having been granted - you are now accountable for the knowledge you have, and you cannot escape it by "disbelieving", because you CAN'T ever again disbelieve...because you know.
That's the difference between believing and knowing, which was your original question. You tried to get to knowledge through belief before, but you could not get there, because what you were believing was not, in fact, true. And the truth - the full truth - you would not have accepted. Even now, you could see the truth through your senses, by studying the physical miracles in depth. But if you do, you will come out the other end discovering that certain things you don't want to believe are part of the truth, and then you're stuck in the same sort of misery that Democrats will be in if Trump wins the election, or Republicans will be in if Hillary does: a reality you don't like, but can't change.
Are you really ready to accept ANYTHING that God shows you. If God reveals himself and you discover that the jihadis are RIGHT, would you become a fundamentalist Muslim? Or are there some truths that are so very unpalatable that, if they are true, you'd rather remain ignorant than find yourself forced to accept the truth of things you absolutely hate?
Don't kid yourself that people who have seen God or the supernatural are merely recounting subjective experiences. The physical miracles are not subjective. They are objective, and can be studied by forensic science - already have been. You CAN know the answers to what you seek. But ask yourself: Do I really want to, if knowledge meant that I would have to reverse my most treasured beliefs about life, liberty and the pursuit of happiness? If the reality of the universe will not make you happy because it conflicts with what you passionately believe now, do you really want the answer? Are you willing to become a Nazi, if God is a Nazi? Are you willing to become a racist, if God is a racist? Are you willing to become a homosexual, if God is a homosexual? Are you willing to do what you hate, if that is what God is?
Are you willing to kill your own child if God demands it of you?
