All official 1924 (and prior) magazine adverts we have show either a mens square, rectangular or tonneau case shape. I don't beleive we have any Bulova magazine adverts showing a round mens wrist watch pre 1925. So how do we interpret this 1924 10AA movement? It would have certainly been housed in a round (or cushion) case and if not a mens then it's possible it came from one of many ladies early models. But, then we have the radium dial and hands which strongly suggests a mens watch.
This is the best evidence we have showing 'this kind of mens watch' was at the very least being advertised and sold by Bulova in 1924.
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I'd like to think it was stamped internally 'BULOVA', but as we have no other examples to compare it to, I think we have to take things on face value for now.