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If you google: "omega 80885889 seamaster serial number" - do some investigating. Compare pics from known dealers with your watch. Look closely at the fonts, date window, Helium valve location, Swiss Made logo, etc.
If it's a known serial that is used on fakes, it should come up early in your searches. The Chinese fakes re-use the same number and forums like this call it out.
To my eye, you watch looks authentic. Under close observation your eyes can play tricks. If you still have concerns, take it to a watchmaker and take photos of the inside. This model is a popular counterfeit target so your concern is understandable. Hang around here and read other strings. Don't panic. If it turns out to be counterfeit and you have no means to return it, refer to our "Noob Tax" thread. We've all been there.