Based on the dial style and hands, I'd say it was from the late 1940's to early 1950's. Unfortunately, the dial on this watch has been refinished incorrectly. The Speedmaster model wasn't introduced until 1957 and is generally found as a chronograph with integrated stopwatch.
The crown is also incorrect. It should be a matching gold tone with an Omega logo in the center.
The movement on your watch is a manual wind and likely is one of the famous 30mm family. Here is a general outline of the movements and the dates produced:
http://www.ranfft.de/cgi-bin/bidfun-db.cgi?10&ranfft&2&2uswk&Omega_265
In order to give you more information, you will need to see a qualified watchmaker to remove the back cover and take a picture of the inside and the movement.
Hope this helps,
gatorcpa
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