It strikes me as dishonest, and needlessly hasty to be a strong atheist, to say as a statement of certain fact that there is no god. However, while it is a needlessly hasty assertion, if there is a god, he is either evil or he doesn't care that they deny his existence. In short, it doesn't matter or at least doesn't matter much if someone is a strong atheist.
The thing is, 'there is no god' is only rational if there is no rational intent by which a good god would hide his existence.
But a simple answer which satisfies such a situation is that God is like us, a person with his own problems and with a need for more perspectives into those problems. In such a setting, it would be most beneficial for people to be atheists, for there to be no proof of his existence or even evidence of any kind, otherwise people would know there was a god and be unable to be self motivated atheists, and incapable of being good to each other for the sake of us rather than some presumed eternal reward. It would poison the game which is best served by being good people.
So there may be a god, but even if there is, I'm fairly certain that he'd want us to not know he was there. Strong atheism says that if there were a god there would be evidence, or at least a simple reason for no evidence. But in the end strong atheism is only slightly less correct than weak atheism, so in the end it isn't worth arguing much about.
I am sorry, but your argument only stands up if you use an incorrect definition of a god.
If the word 'god' has any meaning at all, it has to refer to a being that either created everything, or has a supernatural effect on human lives, or both.
Entities that don't fit this criterion simply are not gods.
Gods are BIG. Even small gods are big, in the same way that even baby elephants are big.
If there is an elephant in your house, you don't need to look particularly hard to find it. Ruling out an elephant in your house is easy - it is not relevant to call upon the concept of falsifiability, nor is it necessary to lift up the cushions on the settee and check underneath.
If God can't be found after a thorough search, then he is not here.
We looked. He isn't here.
The only God not ruled out by this is the creator god who pressed 'Go', and then buggered off. That god is not impossible; just valueless, pointless, and indestinguishable from a natural event or events.
Strong atheism may be untenable if we limit ourselves to pure logic; But logic plus observation makes the position perfectly tenable for any god that fits the definition.
Of course, there might be an elephant hiding in my house, if we are allowed to include mice as elephants. But we are not allowed to do that - it is stupid, dishonest and/or insane.
Any god small enough to exist is too small to qualify for the job.