This is a drawing showing how atmospheres form.
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The Origin of an Atmosphere
There are four ideas for the origin of a planetary atmosphere. Those four ideas are 1. that the planet-elements of which a planet was made decomposed and released the atmosphere, 2. that the atmosphere was drawn to the planet from the gaseous cloud out of which everything came, 3. that comets hit the planet and brought molecules of air with them, 4. that volcanoes erupted and made an atmosphere from gases inside the planet.
Hypothesis #2, in which the original material, which Saturn drew out of the primordial nebula stayed, and forms the atmosphere on Saturn today.
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