Asgorath
Explorer
"If you take the Attack action on your turn," doesn't indicate a specific time. That can happen at any point during your turn, which just so happens to be the same period of time in which you could potentially use a bonus action.
Again, the rules are filled with sentences that have the structure "if X, Y", and often more specifically "If you X, you can Y". This is the way the rules describe a trigger condition, and the condition must be true before Y can happen. This is confirmed by the lead rules designer:
https://twitter.com/jeremyecrawford/status/995043696251842561
"If the existence of X is the condition for the existence of Y, X comes before Y."
This applies for every sentence in the rules that uses that structure. Again, note that I did not say X must be completed -- the condition must simply be true before Y can happen.
If I follow your logic, then as a Ranger with Natural Explorer I can say that there's no timing requirement for me moving stealthily at full pace, the rule just says I can do that. At some point in the future, the "if X" part of the rule will happen, and so that means I get the "Y" part whenever I like.