I agree that showing that there is no God is an impossible task , but you could in theory be capable of showing (at least to your satisfaction) that naturalism is more likely o be true than theism otherwise why do you hold naturalism rather than theism?
Personally, I don't "hold" to naturalism per say.
At best I would say that my current views are compatible with it. But only in the sense that I currently see no reason or evidence to believe that there is something else going on then mere natural forces in the universe.
So it's not so much a position of arguing that "naturalism is more likely true then theism". It's more like a position of "I have no reason to believe theism".
Naturalism though, in the sense that "only natural forces are at work in the universe" becomes the stance by default if and when you have no beliefs in non-natural things or forces in the universe.
But again, I wouldn't say that I have a dogmatic commitment to it.
It just so happens that I currently have no reason to believe in any non-natural things or forces in the universe (be it theism or anything else).
Meanwhile, natural things / forces are
demonstrably at work in the universe.
And if I currently have no beliefs in any non-natural things / forces, then this currently means that I presently only accept natural things / forces to be at work.
But again, I don't reject them a priori at face value. So insofar that I am a naturalist, I'm currently only a naturalist by necessity, not by dogma.
.........................And honestly I think that this leads to a more interesting conversation rather than useless discussions on who has the burden proof
It's not useless at all. See above.
Naturalism is something we all agree on, at least to the extent that there ARE natural things / forces at work in the universe.
So to move on from that, one necessarily has to claim that there is something EXTRA present in the universe.
So it is naturalism + theism. Natural forces PLUS theistic forces.
The one who proposes that "extra" stuff, has a burden of proof to support that extra stuff.
I would say that the idea that there are natural forces at work in the universe, has been demonstrated to everyone's satisfaction by now, wouldn't you?
The claim has already met its burden of proof.
So if you wish to add to that, you're going to have the burden of proof for those extra things.
Failing to meet that burden, means we fall back on only the natural stuff being properly supported.
A theist could also use creative language to avoid the burden proof , I could say things like “I am not convinced that naturalism is true” and thus avoid the burden proof, but I see no benefit in doing that.
Likely because it is a pretty silly thing to do, to deny that there are natural forces and things at play in the universe.