There is no removable case back on these, movement comes out from the front. This would be a watchmaker only procedure.
OP, your dating is off by a decade, this is early 1960s and is not rare. Omega made tis watch with many different dials, so finding an exact match on the internet could be difficult.
If you intend to wear it get it serviced and don't let them polish the case or "restore" the dial.
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