We know by direct measurements that the warming is largely due to greenhouse gases, because we can measure radiation inflow and outflow and see that greenhouse gases are stopping incoming radiation from being radiated out and we can see how much is being trapped.

We know it is the greenhouse gases because we can measure the wavelengths of the incoming and outgoing radiation and see from spectrographs of greenhouse gases that the outgoing radiation falls into greenhouse gas absorption bands.

We can tell that the increase in greenhouse gases over the last couple hundred years is largely from human burning of fossil fuels because the carbon in fossil fuels has a different isotope ratio than that of carbon in living or recently living things. (Volcanic greenhouse gases would also have a similar isotope ratio to fossil fuels but we have sufficient monitoring to detect and account for geologic greenhouse gases).