If you pronounce “caught“ and “cot“ the same way, your dialect of English does not include the sound necessary for the Classical Greek omega. You can approximate this sound by shaping your lips the way you would to say the o in tote, and trying to pronounce the o in cot. This will produce a sound similar to the omega, but still not correct. Now shape your mouth the same way (lips as with the o in tote, tongue as with the o in cot), but draw your tongue slightly back and lower. This time the sound should be much more like the Classical Greek omega.
Compare the following two sounds