How can we see that the federal government is generating and spending fiat money?

Look at the deficit spikes in 2020 and 2021.  The federal government lacked tax revenue to cover federal expenditures, and the lack was three times or more what it had been since 2012.

Deficit means that the federal government spent this money, and it did not come from taxes.  If the money came from debt, then we expect to see spikes in the US debt that mirror the spikes in the deficit.

Look at the federal debt for 2020 and 2021. There is a spike in debt for 2020, but not for 2021. In fact, even the deficit spikes in 2009 and the deficit lows in 2007 do not have mirrored debt increases.   The deficit chart cannot be used to predict the debt growth, which means that they are not directly tied.

Therefore, the federal government operates regardless of tax or debt revenue.

The Federal Reserve describes this here, and explains it here.

The Treasury describes this here in terms of spending must equal taxes and debt in order to prevent inflation.  But, as shown here, there are other options to control inflation.