Thanks everyone for your help!
I have an update: the nut is 3,9 cm so it would put the guitar in between 1966 and 1969 considering the one piece neck and no volute.
I checked the finish with a black light: it all looks good but 1/2 of the back of the headstock. It looks black (touched up).
could it be that someone removed the “made in USA” diciture and changed the serial number to make look a guitar from the 70’s like one from the 60’s?
Did you ever see a 335 from the 70’s with one piece neck and no volute?