If you would read von Mises' "Theory of Money and Credit" or James Grant's "Money of the Mind" you would be less confused about how the gold standard banking regime operated. The money supply wasn't restricted to the amount of gold in the system. 'Credit money', 'bank money', expanded with the economy. Gold convertibility served primarily to keep credit expansion from becoming an engine of inflation.
But, did not Rothbard define inflation as an increase in the money supply? Would not ‘credit money’ or ‘bank money’ be an increase in the money supply, ie, inflation? Besides, how could a bank loan more money than the bank actually itself owned? Would not that bank be insolvent?