In micro, if supply increases and demand remains unchanged, then it leads to lower equilibrium price and higher quantity. Applied to labor it would say increased labor supply lowers wages, or would if it did not also increase demand. The question then is how much does it increase demand. In the infinitesimal limit supply and demand are simply additive and should have no effect on wages. This fails to be a good approximation at large scales however.
Increased labor supply lowers returns for productivity enhancing capital investment and human capital investment, and raises returns for resource producing or saving capital investment, or more simply, lowers the return to labor and raises the return to capital. In doing so, it will lower the growth of the labor supply and increase the growth of capital but this takes time. Increased labor supply increases output but diminishes the growth in output per capita as specialization is overrun by diminishing returns. Now larger markets afford greater specialization and specialization increases growth in output per capita, but specialization is more about technology than population even if population is the source of that technology. The path to growth of output per capita is better sought through technology than population.