Malthus claimed that human population doubled every 25 years unless limited in some way by the amount of available food.

So if there had been some span of time during which the human population was not limited in any way by a scarcity of available food and did not double at that rate, then that would be evidence that directly contradicts his theory.

Are you reading Malthus, or just listening to the little caricature of Malthus in your head and the popular media? Your own link doesn't even say that!

"In the United States of America, where the means of subsistence have been more ample, the manners of the people more pure, and consequently the checks to early marriages fewer, than in any of the modern states of Europe, the population has been found to double itself in twenty-five years."

Basic grammar tells me that Malthus enumerates 2 checks on the population, only one of which has anything to do with food.

Earlier, Malthus writes:

"I think it will be allowed, that no state has hitherto existed (at least that we have any account of) where the manners were so pure and simple, and the means of subsistence so abundant, that no check whatever has existed to early marriages, among the lower classes, from a fear of not providing well for their families, or among the higher classes, from a fear of lowering their condition in life. Consequently in no state that we have yet known has the power of population been left to exert itself with perfect freedom."

If you wish to not allow this, you need to prove both points: about means of subsistence being so abundant no fear exists, and about manners being pure and simple.

And more generally, you don't grapple with the most fundamental point: population growth can be exponential, and resource growth is not.