"The principles we have set down are guides to progress. We claim spiritual progress rather than spiritual perfection." (Page 60, Alcoholics Anonymous)
Preceding this is the instruction to abandon myself completely to God and to take certain Steps fearlessly and thoroughly from the start.
This means that the 'progress not perfection' clause applies only to those who are taking all of the indicated actions promptly and diligently, albeit imperfectly.
The clause is comfort to those who find themselves still having character defects or low mood despite taking all the requisite actions.
For the rest of us, if we are not abandoning ourselves completely to God (as demonstrated by taking the Steps fearlessly and thoroughly), there is no comfort:
"Half measures availed us nothing." (Page 59, Alcoholics Anonymous)