It is possible to create wealth, without paying anyone. For example, if you raise your child, you contribute nothing to GDP, but if you pay someone else to do it, GDP goes up. That's one of the long-standing criticisms of GDP.
The government creates money by spending, and destroys money by taxing. When there's not enough money, the government should spend more and tax less. When there's too much, the government should tax more and spend less. The government sucks money out of the economy only when it taxes more than it spends.
Think of it this way: Suppose everyone paid their taxes in cash, and bales of dollars showed up on the steps of IRS buildings throughout the country. Suppose the government paid for everything with cash, and mailed all the cash from Washington DC.
Should the government gather up all those old dollars, put them on planes, and fly them to DC? Or would it make more sense to shred them, and print new ones?
What difference would it make?