This seems to me to be another case of reading external notions into the rules. I don't think it helps.There you go again thinking take means more than it does. I said that they haven’t taken it. I never said they hadnt started it
The rules don't distinguish starting an action from taking one. I don't think they use the notion of starting an action at all, do they? In 5e - which doesn't use a distinct declaration phase in the way classic D&D tends to and the way that many RPGs and wargames do - to declare an action for one's PC in combat is to take that action. The taking of the action may, in the fiction, be quite complex (eg nocking and loosing several arrows) or quite simple (throwing a single punch). In the mechanics, the taking of the action may require several rolls (eg an Attack action with Extra attacks) or no roll at all (most cases of casting a spell).
The wording of Shield Master is entirely consistent with this absence from the rules of notions of "starting" or "finishing" an action, and with the treatment of taking an action as the core notion. It does produce this interpretive uncertainy - if you must take the attack action before you can do such-and-such, when is it the case that you've taken the attack action? But introducing notions like "starting" and "finishing" - which have no anchor in the actual rules - won't help. It will just be a projection of a prior view of the proper answer to the question.