Not just the government, not really the government at all unless you consider the Federal Reserve Banks lending money to regional banks "government".
The majority of the M0 money supply, that bit of currency we use to get things done in our economy, is created by fiat at any of the ~4500 commercial banks (in the USA). Every time they give out a loan they create the money out of thin air as debt on their balance sheets. They are only required to have a tiny fraction of the money they 'loan'/create (fractional reserve).
If instead of letting only these banks create money, if the new M0 money supply was distributed to ~300 million human people instead of ~4500 corporate people, there'd be plenty for basic income. It'd be universal basic income then instead of commercial bank basic income. And banks could just be banks and get by on their actual services instead of being money machines.
... and that's not even acknowledging what the NY Fed have begun doing since October of last year, 10s to 100s of billions a week swapped for worthless items from corporations who can't pay their bills in Reverse Repo operations: a shallow attempt to pretend it isn't just giving money away (https://apps.newyorkfed.org/en/markets/autorates/temp).