Think of a minimum wage increase as an instant economic stimulus funded by the runaway profits of the major corporations.
People who are struggling to get by on minimum-wage jobs have a lot of pent-up demand - to fix or replace that broken-down car, to put decent groceries on the family table, or to purchase the necessities and tiny luxuries of life.
They’re not going to put that money into hedge funds or Swiss bank accounts. They’re going to buy stuff. When they do, local businesses are going to need people to sell them that stuff. That means there will be more jobs in the community. It also creates more revenue for the smaller businesses that employ low-wage workers, which will help revive real capitalism - the Mom and Pop kind.
As the demand for the stuff they’re buying goes up, the companies that provide it are going to have to hire people to produce it for them. That creates even more jobs.
And every time another job is created, more people buy more stuff - which in turn creates more jobs. That’s the cycle of economic growth. For a real-world example, look at this country’s economic boom after World War II.