The Broker isn't allowed to borrow against client money either - it's client money, partitioned off from the broker's fungible funds, and not the Broker's to offer as collateral.
But debt is the natural answer, and Robinhood did get as much in loans as they can[0].
Suppose a 3% interest rate (which seems high for guaranteed cleared funds), $1 billion for 24 hours is $82,000.