Proof for atheists
Scientists have to accept the existence of the unimaginable nature from the practical example of the unimaginable limits of this infinite universe. Scientists may reject miracles but they cannot reject the unimaginable limits of space. One instance of the existence of an unimaginable entity is sufficient to prove the existence of unimaginable God. Miracles act as supporting evidence of the same concept.
The observable universe is finite in both time and space. What is unobservable is a point of interesting conversation, no more.
Miracles are very widely distributed in the world to give proof for the existence of God to every human being, which is the basic requirement.
Miracles cannot, by their very definition, occur. If they could, they wouldn't be miraculous.
This is an important point, because it is actually quite easy to trick people. Otherwise magicians and their ilk wouldn't be able to ply their trade (honestly or not).
If you pray sincerely in a temple or even in an open place, generally God gives you His answer through a miracle. Many have witnessed this in their lives. Sometimes due to the inevitable fruits of your past deeds, God keeps silent for sometime in spite of your prayers and that time is used for your transformation.
Straight out of the con artist's textbook. If their tricks don't work, it's your fault for not trusting in them enough.
Hence, scientists call this as probability or coincidence of events . Hence, God demonstrates specific miracles through His human form, to meet this twisted interpretation of scientists or atheists. Even devotees and demons do specific miracles.
Your conflation of scientists and demons aside, the sole reason why so many checks are included in an experiment is to guard against such bogus assumptions. To take a simple case, you have some illness, say, non-specific back pain. I wave my hands over you in some ritual. I have magic hands, so I claim. Your back pain decreases.
Is that because my hands have magic powers? Or is it due to the expectations of those concerned in the treatment (the so-called "placebo effect")? Could it be what is called "regression to the mean," that is that the effects of a particular illness often wax and wane naturally, and one is likely to see medical help when the illness is at its worst?
Impossible to tell, unless we include various controls. In this case, it might be someone untrained in the art of magic hands performing a routine similar to my own patented technique. If there is no difference in outcome between the real magic and the fake magic, then we should conclude that I do not, in fact, have magic hands.
God has given a wide coverage for spreading miracles since it involves the very basic issue of His existence.
Oh yes, we were talking about miracles. Miracles cannot happen. This is because if they could happen, it would violate everything that you currently live your life by. For instance, that up is up and down is down. Indeed, what makes miracles miraculous is that they cannot happen. Well, if you are yourself witness to such a miraculous event, think to yourself what is more likely. Did the miracle occur? or were you simply mistaken? If you see a magician saw a lady in half and then reassemble her, did that actually occur? or were you tricked? If you pray for an impossible event to occur, and it does, does that mean that prayer worked, or are your senses merely deceiving you? Is it merely, as you put it, coincidence?
The more likely answer in all of those questions is always the latter: you are deceived, or are deceiving yourself. This, on its own, does not mean that miracles cannot occur, but combined with the previous notion, that is that if they did occur they would not be miraculous (because they could be observed, and so explained), it makes the case extremely weak.
I do not believe that the corollary of all this needs to be spelled out. Nonetheless, I shall. Given that religion, as it is understood in the West, relies on miracles, it is not possible, as a rational being, to believe its claims. That does not mean that one should no longer have faith (or whatever you would like to call it), but one should recognise that said faith is irrational: informally, that it violates every assumption that you otherwise live your life by.
This is largely a paraphrasing of David Hume. You should really familiarise yourself with his writings, because his conclusions are pretty much irrefutable. This has informed proper Christian apologetics ever since; for the better, I might add.