Serial number lines up with the no-T dial and lack of model number between the lugs. Also the big, unsigned crown.
(The 3647 was only available with the earlier-generation dial indices)
You're spot-on that this is an early example, probably dates to about early 1965, maybe even late 1964.
The case is in great condition, which is important with these. Pusher and crystal will indeed be difficult to find but you may have luck at the Chronotrader forum.
This one is still a
in my book!
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