Note that you make an attack with the action, which means before you even make an attack, you've taken the attack action.
"Ah, but you have to make the first attack immediately" you go to say?
Clearly not, since you can take the attack action, then move, then make the first attack.
I don't have much at stake in 5e rules interpretation, but I didn't find yours persuasive. (Which is not to say that I agree with what Jeremy Crawford and [MENTION=6795602]FrogReaver[/MENTION] seem to be saying - read on!)
When you take the attack action, you make an attack doesn't imply that the making of the attack is separate from and subsequent to taking the attack action.
Here's an example sentence to illustrate the point:
When you brush your teeth, you move a toothbrush about and across the surface of your teeth so as to remove foreign substances from them. That doesn't mean that
the moving of the toothbrush is distinct from the brushing of the teeth. Rather, the former is one constitutive element of the latter. I would suggest that, in the case of an attack action, the same is true - making an attack is constitutive of taking the action.
With regard to the movement example -
f you take an action that includes more than one weapon Attack, you can break up your Movement even further by moving between those attacks. For example, a Fighter who can make two attacks with the Extra Attack feature and who has a speed of 25 feet could move 10 feet, make an Attack, move 15 feet, and then Attack again - there is neither statement nor implication that the attack action commenced with the first 10' of movement. The natural reading is that the PC moved, then took the attack action (by attacking) and then - as per the bit I've bolded - took some further movement prior to making the second attack which the attack action entitled him/her to make (in virtue of the Extra Attack class feature).
Combining the movement example with the feat wording -
If you take the Attack action on your turn, you can use a bonus action to try to shove a creature within 5 feet of you with your shield - I think that the most natural reading is that (i) you have to make an attack (thereby taking the attack action) and thereby enliven the ability to use a bonus action (ie in effect we interpolate
then between "can" and "use"), but that (ii) it can come as soon as the attack action has been taken (ie by making an attack) and that could be before
all permitted attacks have been taken.
I can see the argument that the "then" shouldn't be interpolated, but I think not interpolating it creates potential headaches within the context of the D&D framework - eg if I use the bonus action
intending to then follow up with the attack action, and after using the bonus action something happens that prevents me taking further actions (eg some reactive ability paralyses me), then my use of the bonus action becomes retrospectively illegal. Which is not insuperable but I think is weird. Interpolating "then" therefore not only establishes a plausible reading of the natural language but also one that works within the context of the way D&D action resolution unfolds in play.
I can't see
any plausible argument that one has to make
all the attacks to which one is entitled before the ability to use a bonus action is enlivened. Having made an attack, one has taken the attack action (the former, as I have argued, being constitutive of the latter). The fact that you've got more possibilities of making attacks hanging around seems neither here nor there in that respect, and the operation of the movement rules only reinforces that.
So unlike the argument about needing to make
an attack, which I think is supported by both language and the place of the rule within the practical context of gameplay, I think the argument about needing to make
all attacks is supported neither by language nor the practical context of gameplay. If it is being supported on the basis of some sense of "tidiness" in rules interpretation, that seems quite weak to me. Rules should serve gameplay; gameplay shouldn't be subordinated to some abstract (and I would say ultimately hopeless, in any complex rules framework) goal of tidiness.