By what primary method of heat transfer does the sun warm the earth?

Sun warms the earth with Electromagnetic Radiations.

Sun emits out short range radiation in the form of Electromagnetic (EM) Radiation. Our Atmosphere is transparent to EM radiation. It does not heats up the atmosphere but when it collide with the solid objects or particles it is absorbed, reflected or refracted and the object heats up and start emitting radiation in the form of long wave radiation. Our Earth does the same. The long wave radiation emitted by the earth surface is absorbed by our atmosphere and it heats up. Therefore, we can say our atmosphere is heated from below.

Does this your question?

No bc a lot of things r still theories n unproven