The phrase is not about the actual face, but refers to applying cosmetics to enhance appearance. I'll join you for breakfast after I put my face on.
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Informal Use
It's a casual expression, usually not appropriate in formal writing or professional contexts. We're late for the movie because she's still putting her face on.
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Gender Neutral
Primarily used by women, but can be used for anyone applying makeup regardless of gender. He doesn’t start his drag performance until he’s put his face on.