It's a common misperception that that there is a fixed quantity of labor demanded, and that if more than that quantity is supplied, the result is unemployment.
People are not commodities, and the economy is not a zero-sum game. More people willing to work equals more people willing to consume, so the economy expands.
This "lump of labor fallacy[1]" was used when women joined the workforce. The worry was that with only so much work to go around, the additional workers would cause mass unemployment. But we didn't get unemployment, we got a larger economy with a higher standard of living.
The fallacy is also used to argue against immigration, with the fear that immigrants will "steal jobs". It doesn't work that way. Instead of stealing jobs, immigration expands the economy and most people are better off.