The moral argument doesn’t depend on outside knowledge or evidence like the cosmological argument does. It depends on something that we all know and live by: moral law.
We all have a sense of obligation to do the right thing, and that obligation is to a standard outside of and above ourselves. If we had no obligations, we’d do whatever we felt like doing with no thought for principles or for other people. But moral law, like other laws, imposes obligations on us. Whereas man-made laws compel us not to speed or steal, moral law goes even further—it compels us not to lie or be selfish or be indifferent to other people’s needs. Moral law doesn’t come from human government, but we all know it, and we all feel obligated to it.