You are confusing money with notes. At various times and places salt, grain and livestock have been used as money. People were willing to accept these in exchange for almost any other good or service because almost everyone had a use for these commodities other than as money.

You are confusing barter with monetized exchange. Certainly, money evolved gradually from barter, but to call salt “money”, even if it was a common medium of exchange, is to blur the distinction between a barter good and a unit of account, accounting for goods exchanged without being a good exchanged.

Money is a unit of account. Money needn’t have any physical manifestation at all (or hardly any). It can be bits in a computer’s memory or even your memory and mine. The same money can exist in many different memories simultaneously. Money is pure information.

“I can do so without first producing anything of value myself”

Someone must have produced something of value in the present otherwise what are we exchanging?

We can exchange only the promise of future value. You promise to harvest timber and produce lumber. I promise to build houses. A farmer promises to feed us while waiting for a new house. A banker promises to account for all of this production by extending each of us credit to purchase the goods and services of the others (including his own) until houses exist, which could be months after we first transact.

If I trade you a cake in exchange for your promise to provide me two cakes in the future, then I have given up my use of the cake in the present.

You could trade this way, but you needn’t have a cake at all to trade the promise of one. Just as you can accept the promise of two cakes in the future, you can also offer the same promise, and you can even exchange a promise for a promise.

If we both exchange promises, then nothing has been saved/invested because nothing has been produced.

Our resources have been pledged. All investment begins so.

Such contracts can be useful, but no one is loaning/investing anything.

In the housing scenario, we each invest our opportunity to labor in the future, because you promise to harvest timber and produce limber while I promise to build houses and so on.

You are confusing money with notes. At various times and places salt, grain and livestock have been used as money. People were willing to accept these in exchange for almost any other good or service because almost everyone had a use for these commodities other than as money.

“I can do so without first producing anything of value myself”

Someone must have produced something of value in the present otherwise what are we exchanging? If I trade you a cake in exchange for your promise to provide me two cakes in the future, then I have given up my use of the cake in the present. If we both exchange promises, then nothing has been saved/invested because nothing has been produced. Such contracts can be useful, but no one is loaning/investing anything.