The government could spend the money. Or it could give the money to the people (universal basic income) and they could spend it.
This also fixes the inflation problem. Just don't overshoot.
Confiscate $3 trillion from the "rich", and give everyone in the US $10k dollars. What percent would end up back in the banking system after 1 year?
With online banking, etc perhaps once a day.
EDIT:
Actually, if the funds are transferred electronically it would take as long as an ACH transfer takes to get to the new account. The funds are tied up during that but then immediately available to the banking system again.
Banking system is where money lives.
Value lives outside, but the money represented by the value lives on accounts, in databases.
Even cash is just something tracked by central banks as liability (negative account value - because when someone deposits cash they increase one account, and if the bank then deposits that electronic money at the central bank the total money supply must not change, hence cash is tracked separately).
And if you want to take out a loan, it'll still be a risk, since you'll need to make the principle payments, but you'd get a tailwind on the interest paid to you.
I'd be happy to learn where I'm wrong if you have any insight.
Btw the definition of the natural interest rate is "The natural rate of interest, sometimes called the neutral rate of interest[1], is the interest rate that supports the economy at full employment/maximum output while keeping inflation constant"
We have a couple of levers to increase the interest rate. We could reduce inequality to reduce the supply of loan-able funds, we could allow large amounts of immigration to drive up the demand for loan-able funds, or we could keep interest rates high enough that we have a permanently high unemployment.
However I do have a strong worry that natural interest rates are too low for our current inflation. This gives the fed very little room to deal with the next crises. They should probably be targeting an inflation rate closer to 3-4% so we don't run into zero lower bound problems.