Ok, so the oval pushers say 30s or 40s, but the deeper shield didn't come along until the latter. So probably some time from the 40s.

I can't find a match for model or dial, but the movement is definitely genuine and the dial looks ok in the shot of the front too. From what we have to go on, I'd say genuine Heuer but I can't narrow the model down for you unfortunately.

Is the case solid gold or gold-filled? There should be markings on the inside of the caseback (which should also be gold) if it is solid gold. It could be 14 or 18K at that time.