Of course God would know because God is all-knowing, but whether God would use a method that would convince us so there would be no doubt at all would only be true if God was trying to convince us so there would be no doubt at all, but we don't know if that is God's objective.
These atheists argue that God does not exist because we do not see these things. Other atheists argue that God does not exist because if God existed God would communicate directly to everyone in the world.
But none of these atheists have any way of knowing that God would do any of these things if God existed. Moreover, if God does exist and we do not see any of these things happening that means that if God exists God would not do any of these things. So the only logical conclusions one could come to are (1) God exists and chooses not to do any of these things, or (2) God does not exist, because obviously a nonexistent God cannot do anything at all!
But are atheists being unfair in asking or putting forward these objections?
Let's imagine some unspecified idea/claim that we want to examine and we just call this X. Then the first step must be that we have some sort of way to actually verify that X is even possible. What would we expect to see if X is true? and what would falsify X?
If we can't even agree on what we would expect to see if X is true, then we don't really have any way to even approach the claim. Because equally, it would also mean that we have no way to falsify X either then. And by falsifying X I mean, what result of our examination would make X untrue.
So the only logical conclusion is not one of the two options you suggested but (3) We don't know. (1) and (2) are possible conclusions, given the complete lack of a method/agreement on how to even approach the claim in the first place.
When a lot of atheists explain their position of why they are atheists, it is not one of the two conclusions that you presented, but rather the one I did. If we don't know how to even approach the question of whether God exist or not, then there is no logical reason to assume that he does, said in another way, "We see no evidence for God(s) or the supernatural, that would convince us that it is true".
If as you say, we have no way of knowing that God would do any of these things if he existed, then we are not left with a lot of reasons to assume that God exists, because we can't tell the difference between whether God does things or doesn't do things. Said in another way, even if God existed, he might as well not, to us as humans it is the same.
So when atheists say that if God is an intervening one, at least we would have the option to somehow measure/experience some effect if it is something supernatural. That God so far hasn't done this, is not really the fault of the atheists or them being unfair. What other options are there, if we want to examine this?
But even if God is an intervening God, how could we ever know what we were measuring were the effects of God's intervention?
Because God is outside time and space and per definition divine/supernatural. Then it would defy what we consider natural. Meaning that something would happen that we simply couldn't explain as being a natural thing. This is obviously extremely difficult because there are a lot of things we do not know. But science is obviously the biggest none aggressive opponent to religious claims, meaning that science's intention is not to disprove God, but to explain the natural world and as it does that, it leaves less and less room for God.
Some people are "angry/offended" by science, but the fact is that it is the only method we have to examine the natural world and find answers to questions and problems we as humans have. God if he exists, does not provide any answers, so we don't really have an alternative.
Science doesn't intentionally exclude God, in the sense that God must not exist at any cost. Science excludes God, because of its supernatural nature, which is not something science cares about because so far, we have no idea how to even approach such claims, as they in theory can do anything. In theory, everything we know could have been created 2 minutes ago and all of reality imprinted on our brains so we think it is billions of years old. We can't take something like that into account when trying to figure out how the Universe works, and again, we have no reason to assume that it is the case, except for some pointless solipsistic thought experiments. The point is that in theory with the supernatural, everything goes.
That could be why some believers believe in God but it is illogical to say that is why all believers believe in God since that is the fallacy of hasty generalization. These atheists believe that belief is emotional because they are so sure there is no evidence for God. This is their way of saying that no rational person would believe in God so it has to be for emotional reasons.
There can be many reasons why people believe in God, I have no single answer to it. But I think this is an interesting video that is worth seeing if you want to approach an answer, and the fact is that we as humans are "dumb as hell", will probably make more sense after you have watched the video
That is a good point. I do not believe in the fake gods, only the one true God.
Why did so many people believe in those fake gods back in history? It is noteworthy that there are less people who believe in them in the modern age and the bulk of people believe in the the one God of the Bible, the Qur'an, and the Writings of Baha'u'llah. Still, that is only about 55% of the world population, so there are many other God conceptions out there and many people who still believe in multiple gods.
Again I think the video will somewhat address this issue as well. But you see the issue, with drawing the conclusion that some Gods are fake when just above, you admit that there is no way to know what God do and doesn't do? It doesn't seem to be a logical conclusion