The colonization of bacteria that eat ammonia takes time. The addition of bottle bac gives the colonization effort a huge boost with numbers of bacteria to develop the slime coat on the rock surfaces that eats the ammonia. There's a guy on here
@brandon429 who has written a lot about this topic, bacteria + time = cycled tank, without fail. If you start with live rock time to add fish is reduced, perhaps to zero if you have enough live rock. Dry rock requires time to grow but it's fairly quick.
The API is the other part of equation. Those Ammonia tests are nortorious for false high readings in tanks with zero ammonia and cycled. 4 weeks is plenty of time, at 4.5 you are ready to add fish, slowly is best.