That assumes that the number of available jobs is perfectly-sized and fixed, and that there's no other work that could be done (or no under-employed, existing work that could be done better) if we had more workers. That would seem not to be true.
No it assumes the exact opposite of a fixed number of jobs-- it assumes the other work wasn't being done because wages were too high to make it profitable, but as the workforce grew the price of labor dropped until employers wanted to hire into those jobs. That's the whole idea behind supply and demand.
How would you explain the stagnant wages of the last 4+ decades compared to the massive economic growth? I don't think there's much evidence that the relationship between labor supply and economic growth is anywhere near one-to-one (e.g. one more person working means their wage is added to the volume of labor demand).