PHB192 Actions in Combat: "The most common action to take in combat is the "Attack action", whether you are swinging a sword, firing an arrow from a bow, or brawling with your fists. With this action;
"you make one melee or ranged attack. See the "Making an Attack" section for rules that govern attacks."
PHB194 Making an Attack: "If there's ever any question whether something you're doing counts as an attack, the rule is simple: if you're making an attack roll, you're making an attack."
Since a shove requires an attack role it can by itself initiate the "attack action" and according to these these rules it can also occur anywhere in the sequence.
So, in order to do an attack action, you have to make one melee or ranged attack, correct? Otherwise, it is not an attack action. To make a melee or ranged attack, you have to make an attack roll, correct? Otherwise, it is not an attack.
The problem for your interpretation is that the shove attack is gained by the attack action, but it doesn't occur if there is no attack action. The attack action has to occur. An attack roll from that particular action has to occur in order to trigger the shield mastery bonus action. Without the attack action and hence the attack roll, no shield bonus occurs. Horse before the cart.
Your interpretation seems to imply that just declaring an attack action is the same as making one.