Yes, the burden of proof is on the theist. They have the positive claim. But that does not mean we get to run away claiming victory just because they have not come forward with evidence for god.
Science and logic simply do not work that way. Lack of evidence is not proof on nonexistance.
A fact would be that I do not believe in god. A fact would be that there is insufficient evidence to compell all atheists to accept the claim of god's existance. But we simply do not have evidence of god's nonexistance. We cannot prove negatives such as this. It's why we don't use the word proof in science (if we are using terms properly).
Science is an evidentiary process. It can only really chip away at things it finds to be false and promote theories about what it suspects is true. This creates a couple of problems. It can never prove anything in the absolute and it cannot prove a negative. We can provide ample evidence that there are no smurfs in the universe but unless we can search all of the universe in it's entirety in one moment we simply cannot come up with evidence of the nonexistance of smurfs.
Science and reason give us tools to increase our certainty of things. But they cannot give us absolute certainty. It is deliberately an open ended process. We must always remain open to new evidence that may overturn our conclusions. No matter how certain we are of them there is always a possibility that we got it wrong. This is the very thing that drives science and gives it it's credibility. It is self correcting. It can admit when it is wrong. But the price is never being absolutely certain.
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