Calm down
If a loose definition is used then during World War, almost all air-crews wore plate carriers in the form of M-2. It was a flak jacket with inserts of aluminum plates.
But if we keep our definition limited to just non-metallic plates then here's T-65-2 plate carrier from 1966; pretty much reminiscent of the modern carriers.
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This was extremely expensive at that time given no-one knew that something like this can be even done so roll-out was bit slow. First air-crews got these, then obviously the Tiers-Is and then everyone.