I mean what constitutes "proof" for you? Does it need to be void of abstraction and indirect causal chains? Because if so, good luck. If you allow for this I think there's plenty of strong evidence for it and many others have written about this. I mean we see these same trends through scale and history, so it is not as far of a stretch as I think many of those that are quick to dismiss the hypothesis claim. Absolutely nothing in our modern world will be adequately explained without abstraction and consideration of complex interacting chains (this even includes the conflicts in Ukraine and Gaza. While there's often claimed a clear aggressor the truth is that aggressions have been taken by all parties over a long time. To be clear, I'm not saying any specific party is justified in their actions nor am I saying all parties are equal. But the ambiguity is simply because I don't want to start a long complex off topic thread over these current hot topics, not because of a lack of alliance).
But given your response I think there maybe confusion as to what is being referred to when discussing "Long Peace." It is not the absence of war, it is the absence of __direct__ war between __major powers__. This may not be clear since being born into long peace (as presumably you are <80 years old), is that this is the only type of war we've experienced and directly know. Prior to this, major powers directly fought, and quite frequently. Usually this is discussed with respect to Europe but the general trend is true elsewhere and similar patterns exist on the Indian subcontinent as well as Asia and even in the Americas. It is also worth noting that even wars between these smaller powers has decreased (likely due to the connections with larger powers and how many are unwilling to go to direct war with larger powers).
While sanctions certainly aren't absolutely effective, that's not entirely the point either. The point is to make these actions more resource intensive, not impossible. Even our direct discussion about NK is illustrative of this, as they have to spend resources to be covert and it is clear that this sub-sub-...-contracting would be more economically fruitful were they not have to operate though these sidechannels and could operate directly. I mentioned in another comment about how society operates in unstable equilibria and how this is why there's a clear imbalance between red teams and blue teams, where the blue team has a much harder job. The same is true here too. Just because they can bypass sanctions also doesn't mean they are ineffective. It is important to not binarize things.
And to clarify, globalism isn't necessarily American dominance, but rather that countries are negotiating on the economic table. While described by Pax Americana there have also been Pax Britannica, Pax Romana, and others which saw similar trajectories but never before at the global scale as the world was not operating globally previously. In that sense it is often explained how this trend has happened through human history and correlates heavily with globalization.
If you're going to make an argument I'd suggest one about delay, as (in my opinion) one can more easily create a stronger argument about how the proposed explanations of long peace (note that there is not a singular one, and no serious person believes a singular factor is the cause, as should be apparent by the initial lines in my comment), rather displace the inevitable wars and death. That these result in growing tensions where the pressures accumulate and result in large scale and more horrible war. But we must also explain the much longer historical trend and it isn't unreasonable to believe that issues like these are more akin to a damped oscillator rather than a clear monotonic decay (which is measured to not be true but also confounded with the suggested argument).