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The OED has a draft entry (2002) for "in the zone" that says its origins are chiefly US sport. Its earliest citation is a 1976 San Francisco Chronicle article about tennis:

Tennis players speak reverently of the mystical atmospheric condition known as ‘The Zone’ Passing shots chip away at the lines, first serves pop in and mistakes simply don't materialize.

The next citation is from 1990, and refers to the more general creative sense.

Performers, surgeons, or creative artists..find that most important parts of their lives occur when they are ‘in the zone’.

Source is the New Age Journal. Notice how it is no longer capitalised.