Although not the type of bracelet typically seen on a Seamaster 600 it certainly could have been fitted from new. There should be numbers on the folding part of the clasp, a photo of this would be helpful.
Looks like a reference 135.011, mid 1960s, the serial number on the movement will help date your watch more closely.
Have a watchmaker remove the back and take some nice clear photos of the inside of the back and movement.
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