If it were true that without debt there'd be no money, then it would be impossible to have an economy where there was money but no debt. In fact such an economy is perfectly possible. People would just deposit collateral at banks and have their accounts credited with $X, $Y or $Z and with a view to conducting day to day transactions. That would give rise to short term debts in the sense that the amount in each person's account would rise above and fall below $X, $Y or $Z for short periods (e.g. there'd be a rise when people got their salary). However, there'd be little point in banks charging interest on those short term debts. Plus in such an economy there'd be no long term debts like mortgages, which is what advocates of the "without debt there'd be no money" idea really have in mind.
When commercial banks grant loans (i.e. create debt) they create money. That point has been explained by the best economics text books for decades and is confirmed in the opening sentences of this Bank of England publication.
You might conclude from that that without debt there'd be no money. Indeed, the latter claim is often made by those advocating a change to the bank and monetary system.
If the latter claim were true, it would follow that it would be impossible to have a system where there was money but no debt. Of course that's a bit of a hypothetical system or society, but a culture where no one wished to go into debt is certainly a theoretical possibility: i.e. everyone would want to pay cash on the nail for everything. So let's examine such a hypothetical society to see if it's possible for commercial banks to supply a form of money without anyone going into debt.
Incidentally, CENTRAL banks create or issue a form of money which can well be argued to be "debt free", but let's ignore central banks: we're concerned here just with COMMERCIAL banks.
A barter economy.
So, let's start with a barter economy where a commercial bank or series of commercial banks set up in business. They offer some wondrous new stuff called "money" to anyone banks regard as credit worthy (perhaps because they've deposited collateral or perhaps not). The actual units making up that money doesn't matter: make it an ounce of gold if you like, and each unit is called a "dollar".
And let's say just to keep things simple that EVERYONE in this hypothetical society (including employers) wants $1,000 to enable them to do day to day transactions in a more efficient manner than under barter. So $1k is credited to everyone's account.
Now at that stage, i.e. before any spending starts, is there any debt? The answer is "no". Or to be more accurate, there are two equal and opposite debts: first, banks owe everyone $1k in that money in your current / checking account is a debt owed to you by your bank. Second, there's a debt owed by everyone to their bank: that's everyone's undertaking to repay the $1k to the bank at some stage. (That "equal and opposite" scenario is actually set out in economics text books: it's not some strange new invention of mine.)
So, before any spending starts, there is no net debt. That is, no REAL RESOURCES or goods and services have moved from one person to another or from people to banks or from banks to people. All that's happened is that some book-keeping entries have been made.
As to physical cash (dollar bills, pound notes, coins etc.), bank customers might want some of that. But there again, creating and issuing paper notes involves virtually no consumption of REAL RESOURCES: printing bank notes costs next to nothing.
Incidentally, I have of course assumed that commercial banks ARE ALLOWED to issue their own bank notes, an activity that was stopped in the UK in 1844.
As soon as spending starts, remember that any money leaving one person's account arrives someone else's account (or in someone else's wallet in the case of physical cash). Thus the AVERAGE stock of money possessed by citizens in this society always remains at $1k.
Incidentally, to keep things simple, I'll assume from now on that all transactions are done by check or debit card rather than physical cash.
Also bear in mind that assuming everyone has enough regular income (wage, pension, etc.), to enable them to pay their way, the balance on their account will on average over a few months or a year remain at $1k. That is the balance will tend to rise above $1k on receipt of their wage, and then fall below $1k over the next 30 days assuming wages are paid monthly.
But where's the long term debt? There isn't any!
There are of course a series of SHORT TERM debts: i.e. if someone spends $X they're temporarily in debt to the tune of $X. But assuming that citizens of this country are just after money or LIQUIDITY, i.e. enough money to do day to day transactions, the latter individual's bank balance will be $X ABOVE $1k as often as it is BELOW $1k.
Charges made by banks.
In the above scenario, banks would clearly have to charge for ADMINISTRATION costs, e.g. the cost of checking up on the value of collateral. Indeed in the real world, there is often a "set up fee" or something of that description charged by banks when arranging a mortgage. As to INTEREST, there's not much point in banks charging interest because banks would owe each customer money as often as customers owe banks money. Of course banks COULD CHARGE interest to those whose bank balances fell below $X, but then people would by the same token be justified in demanding interest from banks when the balance on their accounts was ABOVE $X.
Certainly if banks WERE TO charge interest, the NET AMOUNT of interest over the year charged by banks would be zero. (Incidentally, I'm assuming there that any interest charges are what might be called "genuine interest", that is a charge for money owed, as distinct from administration costs)
Long term debts.
In contrast to the above SHORT TERM debts, there are LONG TERM debts, like mortgages which very definitely DO INVOLVE interest. And it's that sort of debt that people have in mind when they claim that "without debt there'd be no money". But as I've just hopefully demonstrated, those sort of long term debts are not needed in order for commercial banks to create money. And as to any interest that is charged on short term debts, that doesn't make much sense. So the payment of interest is not needed either, for commercial banks to issue a form of money.
Moreover, long term loans tend to be matched by long term deposits, i.e. so called "term accounts" (maturity transformation apart). And so called "money" in term accounts is often not counted as money (depending on the exact length of the term). Thus even the claim that long term loans create money is questionable.