China is an immensely populous country, especially before the establishment of the "one-child" policy. You know, "more children means more sources of income for you" essentially was the predominant mindset. The fact that Men were conscripted at a young age to form militia was nothing out of the ordinary as well, more so when you're impoverished, in which at that time, was the case for most people. Also, there's the possibility of reinforcements from neighbouring states or provinces, so yeah, rounding up 400k for large skirmishes especially against Qin, which was the 2nd largest state at the time, is not a difficult feat when given the right relations and conditions.