Not much at all. Most money has been just numbers on some ledger for a long time. And what people call money is just written promises on a piece of paper. The gold standard where those pieces of paper could be exchanged for that is also history at this point. And people physically moving lots of gold around as a means of payment of course stopped being a thing centuries ago.
To what extent is inflation influenced by the physical money supply? Isn't it just banks that control it at their discount window?