The heat you feel is radiation from the sun.
Stand in front of a bonfire. You will feel the heat radiation from the fire. Imagine how big and hot a bonfire the sun must be to feel as hot as it does when it’s so far away!
The atmosphere is transparent, which means that it (almost) doesn’t interact with the sun’s light. That’s why sunlight (almost) cannot heat up the atmosphere. Instead, the atmosphere is heated by the earth which is heated by radiation from the sun.
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