Saturn was formed around billion years ago along with Jupiter. After which it had enough time to form moon which can break into rings.
Then why is it said that Saturn's ring are of recent origin - about few million years ago?
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The 4.something-billion-years-old fits in with one of the two theories of the rings' formation - that Saturn swept up material from the protoplanetary disk. The date makes sense, because there's no way the disk would last for billions of years.
The newer date does fit in with the moon-torn-apart hypothesis, which is perhaps the dominant hypothesis. The hypothetical progenitor moon could have been torn apart at any point between Saturn's birth and the present day. "A few hundred million years ago" fits in reasonably well.
I should add that all the theories surrounding the rings' formation have reasonable evidence in their favor, though there's quite a lot for the 4.something-billion-years theory (see here, here and here). Thank you, Cassini!