Respectfully, time series analysis involves the use of statistical techniques which have been designed precisely to tease out these kinds of correlations. So what you claim to be impossible is not only statistically possible, but in fact constitutes mainstream econometrics.

There is a clear consensus that fiscal stimulus in war spending played a key role in pulling the United States back to full employment. There is also a clear consensus that the gold standard served as a transmission mechanism for deflationary pressures internationally. If you do not believe this, I'd challenge you to find even a single NBER paper that argues otherwise.