The IMF was a response to pegging all world currencies to the US dollar. Before that, the gold standard was apparently supposed to automatically redress large trade deficits and arrears in payments between nations. But after WW2 a new regime evolved, and gradually the IMF evolved from this into something that ensures standardised exchange rate and monetary policies conducive to free trade, and to provide short term funding for trade deficits, etc. Basically stability of the international financial system
Bottom line, it seems to me, is you can probably get something like it after a big shakeup like the Napoleonic wars, if Britain pushes for it on the basis of free trade (after all the BIS was established in 1930 before most nations went off the Gold Standard. But you won't get something like today's IMF until the principle of gold-backed currency is abandoned, which is unlikely to happen.
That being said, another possible time PoD be if the Depression of 1873 is deeper and more severe. This may or may not force nations from gold to fiat currency in order to combat deflation, but what it will do is press home even more than OTL the recognition that the global capitalist economy is linked, and systemic robustness is important to make sure the rising tide lifts all boats.
Your problem for this WI is that you need the foremost political and economic thinkers in the 19thC to begin to produce a large amount of work in a relatively short space of time that all tends towards the same conclusion: that nations need to cooperate with their domestic financial and economic policies to benefit themselves as well as all other states, and to help each other out when one or some are undergoing difficulty, to prevent a national depression that could eventually trigger a more generalised, worldwide one. And then you need to give policymakers a big enough reason to actually pay attention to these developments and synthesise them across multiple disciplines, and then come up with something this visionary. This would basically be proto-Keynsian stuff, combined with the kind of Internationalism and harmony among nation states we didn't really see that much before the Post-WWI era, so it's a tall order to make it happen decades ahead of schedule, but still possible I think.