Why would this money increase inflation? It wasn't earmarked for consumer spending in the first place.
The government could have printed a bunch of money to build a giant nuclear is solar plant, and then have a revenue generating, publicly owned asset at the end of it. Instead the government printed the money to prop up existing asset prices.
Just like increasing a company's cap table, there's nothing wrong so long as the new money is converted into a new asset of value that remains in the company's balance sheet.
In fact, a well managed money printing event should dilute private wealth and replace it with public wealth, which is the sort of green new deal I support.